# Question
Title: The real treasure was the numbers we made along the way
Your task is to write a program, function or snippet (yes, snippets are allowed) that simply outputs an integer. *However*, you must be able to separate your submission into prefixes that *also* produce distinct integers. You cannot use any bytes that have appeared in previous prefixes. For example, we can have the prefixes:

```
1         # 1    (Now we can't use 1)
1-6       # -5   (Now we can't use - or 6)
1-6/3     # -1   (Now we can't use / or 3)
1-6/3+0xA # 9    Final submission

```

## Rules

* Your goal is to create to try and create the most unique integers, while keeping them close to zero.
    + The scoring system is `((number of unique integers)**3)/(sum of absolute values)`, where the higher your score, the better. The above example scores \\$(4^3)/(1+\lvert-5\rvert+\lvert-1\rvert+9) = 64/16 = 4\\$.
* There should be at least two unique integers (no dividing by zero!)
* Please format your answer similar to:

```
# Language, \$(4^{3})/16 = 4\$

   1-6/3+0xA (the full program)

```
* Mention if your submission is composed of snippets that evaluate to a value, functions or full programs.
* List each of the prefixes and (optionally) an explanation for how they work.

# Answer
# TI-BASIC (TI-84+ CE), \\$238^3/14161 = 952.0\\$

```
118-length("+×/ABCDEFGHIJK...

```

The 256 bytes in TI-BASIC break down thusly:

* 240 bytes are one-byte tokens that can be quoted
* 11 are the start of two-byte tokens
* 2 are unused
* The remaining 3 are the `"`,, and newline characters which break strings.

The string contains all 237 allowable bytes in the first category not already in `118-length(`.

The program calculates 238 distinct integers, ranging from 118 down to -119. The score is therefore $$ \frac{238^3}{\sum\_{n = -119}^{118} |n|} = 952.$$
> 20 votes

# Answer
## vim, 14³ / 53 = 51.77

```
i10<esc>X<c-x>r2hx<c-a>Pa<del>4<c-c>d^s5<c-o>I-<c-o>$<c-o>C6<c-h>7

```

Try it online! (all prefixes)

Breakdown:

```
i1                  1
0                   10
<esc>X              0
<c-x>               -1  <c-x> decrements
r2                  -2
hx                  2   hx is X, but we've already used that
<c-a>               3   <c-a> increments
P                   -3  paste the - from two steps ago
a<del>4             -4
<c-c>d^             4   <c-c> is an <esc> alternative
s5                  5
<c-o>I-<c-o>$<c-o>  -5  <c-o> allows a single normal mode input
C6                  -6  trailing <c-o> from previous line used here
<c-h>7              -7  <c-h> = backspace

```
> 13 votes

# Answer
## Lenguage, 256³ / 16384 = 1024

The source code of the solution can be described as follows:

```
183662808731984092                                         0x00 bytes
4775233027031586288                                        0x01 bytes
27                                                         0x02 bytes
81                                                         0x03 bytes
128931291729852829668                                      0x04 bytes
108                                                        0x05 bytes
648                                                        0x06 bytes
81                                                         0x07 bytes
2079                                                       0x08 bytes
27                                                         0x09 bytes
3481144876706026401009                                     0x0A bytes
108                                                        0x0B bytes
2808                                                       0x0C bytes
27                                                         0x0D bytes
17496                                                      0x0E bytes
81                                                         0x0F bytes
2079                                                       0x10 bytes
27                                                         0x11 bytes
56106                                                      0x12 bytes
756                                                        0x13 bytes
93990911671062712827216                                    0x14 bytes
108                                                        0x15 bytes
2808                                                       0x16 bytes
27                                                         0x17 bytes
75789                                                      0x18 bytes
756                                                        0x19 bytes
474552                                                     0x1A bytes
27                                                         0x1B bytes
81                                                         0x1C bytes
56025                                                      0x1D bytes
756                                                        0x1E bytes
1514835                                                    0x1F bytes
20439                                                      0x20 bytes
2537754615118693246334805                                  0x21 bytes
108                                                        0x22 bytes
2808                                                       0x23 bytes
27                                                         0x24 bytes
75789                                                      0x25 bytes
756                                                        0x26 bytes
2046276                                                    0x27 bytes
20439                                                      0x28 bytes
12812877                                                   0x29 bytes
108                                                        0x2A bytes
729                                                        0x2B bytes
2079                                                       0x2C bytes
27                                                         0x2D bytes
1512648                                                    0x2E bytes
40920957                                                   0x2F bytes
1689866867948183303767857                                  0x30 bytes
66829507740256534347823839                                 0x31 bytes
2808                                                       0x32 bytes
27                                                         0x33 bytes
75789                                                      0x34 bytes
756                                                        0x35 bytes
2046276                                                    0x36 bytes
20439                                                      0x37 bytes
55249425                                                   0x38 bytes
551880                                                     0x39 bytes
345947652                                                  0x3A bytes
2916                                                       0x3B bytes
27                                                         0x3C bytes
19656                                                      0x3D bytes
56133                                                      0x3E bytes
40842225                                                   0x3F bytes
1104865839                                                 0x40 bytes
45626405434600949201732247                                 0x41 bytes
1804396708986926427391243545                               0x42 bytes
27                                                         0x43 bytes
75789                                                      0x44 bytes
756                                                        0x45 bytes
2046276                                                    0x46 bytes
20439                                                      0x47 bytes
55249425                                                   0x48 bytes
551880                                                     0x49 bytes
1491734448                                                 0x4A bytes
9355487364                                                 0x4B bytes
78732                                                      0x4C bytes
756                                                        0x4D bytes
530685                                                     0x4E bytes
1515591                                                    0x4F bytes
1102740075                                                 0x50 bytes
29831377653                                                0x51 bytes
1231912946734225628446770696                               0x52 bytes
48718711142647013539563576444                              0x53 bytes
2066715                                                    0x54 bytes
55801305                                                   0x55 bytes
1506635235                                                 0x56 bytes
292874988897                                               0x57 bytes
2125764                                                    0x58 bytes
14348907                                                   0x59 bytes
40920957                                                   0x5A bytes
29773982025                                                0x5B bytes
33261649561824092773510005450                              0x5C bytes
1315405200851469365568216563988                            0x5D bytes
55801305                                                   0x5E bytes
1506635235                                                 0x5F bytes
7948303851537                                              0x60 bytes
57395628                                                   0x61 bytes
387420489                                                  0x62 bytes
1104865839                                                 0x63 bytes
803897514675                                               0x64 bytes
898064538169250504884770147177                             0x65 bytes
35515940422989672870341847227676                           0x66 bytes
1506635235                                                 0x67 bytes
40679151345                                                0x68 bytes
214604203991472                                            0x69 bytes
1549681956                                                 0x6A bytes
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29831377653                                                0x6C bytes
24001245795414021635055080475036                           0x6D bytes
246496735155742018538946394995                             0x6E bytes
958930391420721167499229875147252                          0x6F bytes
40679151345                                                0x70 bytes
5795411844856032                                           0x71 bytes
41841412812                                                0x72 bytes
282429536481                                               0x73 bytes
805447196631                                               0x74 bytes
648033636476178584146487172825972                          0x75 bytes
108                                                        0x76 bytes
6655411849205034500551552664784                            0x77 bytes
25891120568359471522479206628975804                        0x78 bytes
1098337086315                                              0x79 bytes
156484875126743748                                         0x7A bytes
21747074309037                                             0x7B bytes
17496908184856821771955153666301244                        0x7C bytes
108                                                        0x7D bytes
2808                                                       0x7E bytes
27                                                         0x7F bytes
81                                                         0x80 bytes
179696119928535931514891921949087                          0x81 bytes
699060255345705731106938578982346708                       0x82 bytes
4225121283523411674                                        0x83 bytes
472416520991134187843376319996477587                       0x84 bytes
108                                                        0x85 bytes
2808                                                       0x86 bytes
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75789                                                      0x88 bytes
108                                                        0x89 bytes
729                                                        0x8A bytes
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27                                                         0x8C bytes
4851795238070470150902081892625349                         0x8D bytes
18874626894334054739887341632523361116                     0x8E bytes
114078274655132115171                                      0x8F bytes
12755246066760623071771160639904894849                     0x90 bytes
108                                                        0x91 bytes
2808                                                       0x92 bytes
27                                                         0x93 bytes
75789                                                      0x94 bytes
756                                                        0x95 bytes
2046276                                                    0x96 bytes
2916                                                       0x97 bytes
27                                                         0x98 bytes
19656                                                      0x99 bytes
56133                                                      0x9A bytes
130998471427902694074356211100885179                       0x9B bytes
854006569949556303994892977044130020645                    0x9C bytes
108                                                        0x9D bytes
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756                                                        0xA1 bytes
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55269864                                                   0xA3 bytes
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756                                                        0xA5 bytes
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3536958728553372740007617699723899860                      0xA8 bytes
23058177388638020207862110380191510557388                  0xA9 bytes
108                                                        0xAA bytes
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27                                                         0xAC bytes
75789                                                      0xAD bytes
756                                                        0xAE bytes
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55249425                                                   0xB1 bytes
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40920957                                                   0xB5 bytes
622666287378897486676257185943063330345696                 0xB6 bytes
108                                                        0xB7 bytes
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75789                                                      0xBA bytes
756                                                        0xBB bytes
2046276                                                    0xBC bytes
20439                                                      0xBD bytes
55249425                                                   0xBE bytes
1492286328                                                 0xBF bytes
40291730856                                                0xC0 bytes
57395628                                                   0xC1 bytes
387420489                                                  0xC2 bytes
1104865839                                                 0xC3 bytes
16811989759230232140258944020462709919333792               0xC4 bytes
108                                                        0xC5 bytes
2808                                                       0xC6 bytes
27                                                         0xC7 bytes
75789                                                      0xC8 bytes
756                                                        0xC9 bytes
2046276                                                    0xCA bytes
20439                                                      0xCB bytes
55249425                                                   0xCC bytes
551880                                                     0xCD bytes
1491734448                                                 0xCE bytes
40291730856                                                0xCF bytes
1087876733112                                              0xD0 bytes
1549681956                                                 0xD1 bytes
10460353203                                                0xD2 bytes
29831377653                                                0xD3 bytes
453923723499216267786991488552493167822012492              0xD4 bytes
2808                                                       0xD5 bytes
27                                                         0xD6 bytes
75789                                                      0xD7 bytes
756                                                        0xD8 bytes
2046276                                                    0xD9 bytes
20439                                                      0xDA bytes
55249425                                                   0xDB bytes
551880                                                     0xDC bytes
1491734448                                                 0xDD bytes
40291730856                                                0xDE bytes
1087876733112                                              0xDF bytes
29372671794024                                             0xE0 bytes
324270949293                                               0xE1 bytes
805447196631                                               0xE2 bytes
12255940534478839230248770190917315531194337311            0xE3 bytes
76545                                                      0xE4 bytes
2066715                                                    0xE5 bytes
55801305                                                   0xE6 bytes
1506635235                                                 0xE7 bytes
832318279426764                                            0xE8 bytes
21747074309037                                             0xE9 bytes
330910394430928659216716795154767519342247107424           0xEA bytes
2066715                                                    0xEB bytes
55801305                                                   0xEC bytes
1506635235                                                 0xED bytes
22472634223673946                                          0xEE bytes
8934580649635073798851353469178723609411678244474          0xEF bytes
55801305                                                   0xF0 bytes
1506635235                                                 0xF1 bytes
40679151345                                                0xF2 bytes
606761124039196515                                         0xF3 bytes
241233677540146992568986543667825537454115312600825        0xF4 bytes
1506635235                                                 0xF5 bytes
40679151345                                                0xF6 bytes
6513309293583968799362636679031305893812560835614495       0xF7 bytes
40679151345                                                0xF8 bytes
1098337086315                                              0xF9 bytes
175859350926767157582791190333845259132939142561591365     0xFA bytes
1098337086315                                              0xFB bytes
4748202475022713254735362139013821996589386504264297360    0xFC bytes
29655101330505                                             0xFD bytes
128201466825613257877854777753373193907913435615136028720  0xFE bytes
3461439604291557962702078999341076235513663562296408699075 0xFF bytes

```

Each run of identical bytes combined with the previous runs constitutes a prefix, and the full program is all the strings described above concatenated.

This is an optimal score. (The programs print all numbers from -127 to 128 inclusive.)

To create this answer, first, I copied the Java answer here for generating brainfuck programs to print a string. I ran it with this `main` function:

```
public static void main(String[] args) {
    for (int i = -127; i <= 128; ++i) generate(""+i);
}

```

Then, I ran this Ruby script to generate the human-readable text shown here:

```
#!/usr/bin/ruby
nums = File.open('f').map do |line|
    line.chomp.sub(/^\+/, '>+').chars.map{|ch|
        '+-><.,[]'.index(ch).to_s(3).rjust(3,?0)
    }.join.to_i 3
end
puts ([0]+nums.sort).each_cons(2).map.with_index{|x,i|"#{x[1]-x[0]} 0x#{i.to_s(16).rjust(2,?0).upcase} bytes"}*"\n"

```

The largest program is 3594571896764310192036774345469579167648804468538578264427 bytes long (and prints `-90`).
> 12 votes

# Answer
# Javascript, \\$(111^{3})/2530 = 540.5656126482213\\$

```
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```

(Credit to this interesting utility for the conversion.) The above effectively evaluates into the following code:

```
(new Proxy({},{get:(a,p,b,n=p.length+3)=>n%2?(n-1)/2:-n/2})).$0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ_abcdefghijklmnopqrstuvwxyzÀāłƃǄȅɆʇˈ̉͊βόЍюҏӐԑՒ֓הٖؕڗۘܙݚޛߜరᡡⱱ㣣䤤奥榦秧訨驩ꪪ뫫쬬흝ﯯ&''|""**"",~{}

```

...which creates a proxy that converts the length of a property name into a number. The first prefix ends one character after the `.`, and uses only 6 unique characters, excluding the `.$`. The next 63 slices append 63 other single-byte characters which are valid in JS object property names. The next 44 slices append two-byte valid characters made up of unused bytes. The final slices append `&''`, `|""**""`, and `,~{}`. The first slice returns `-2`, the second `2`, then `-3`, then `3`, `-4`, `4`, `-5`, etc. up to the last three slices which are `0`, `1`, and `-1`.
> 8 votes

# Answer
# Brain-Flak, \\$4^3/4=16\\$

For this one we use brain-flak snippets so we are concerned with the value not what they do.

Complete program:

```
<>(())[[][][]]{}

```

Prefixes and output

```
 0 : <>
 1 : <>(())
-2 : <>(())[[][][]]
-1 : <>(())[[][][]]{}

```

Try it online!

## Explanation

This is probably the best a brain-flak answer can get since we've used up all the character Brain-flak cares about, and we can't cluster the numbers closer to zero.

The first snippet is `<>`, `<>` changes the stack but otherwise evaluates to zero, so we start with zero. From here we add `(())` this makes one. We could have just done `()`, because that is also one, but if we push a one now we will be able to recall it later with `{}` and `[]`. This is pretty much the only way `{}` and `[]` can create value so we do that. Since there is one thing on the stack `[]` counts as a 1 so we subtract 3 from the total with `[[][][]]` bringing us to -2. Lastly we use `{}` to pop the one we pushed earlier bringing us up to -1.
> 4 votes

# Answer
# Python 2, ~~32~~ ~~34.7~~ ~~40~~ \\$(11^{3})/32 = 41.59375\\$

After two hours of trial and error I finally got all integers from `-4` to `+5` (and `7`).

```
0^cmp('','_')&3+1/~9*2-[-[-[[]==[]][[]==[[]]]][[]==[[]]]-[-[[]==[]][[]==[[]]]][[]==[[]]]-[-[[]==[]][[]==[[]]]][[]==[[]]]-[-[[]==[]][[]==[[]]]][[]==[[]]]-[-[[]==[]][[]==[[]]]][[]==[[]]]][[]==[[]]]|6<<7<<7>>8>>8and 5

```

This is a snippet with the following prefix snippets:

```
# -1
cmp(cmp,())
# +3 = (-1) & 3
cmp(cmp,())&3
# +7 = 3 + 4
cmp(cmp,())&3+4
# +2 = 3 + (-1) = 3 + floor(4/-10)
cmp(cmp,())&3+4/~9
# +1 = 3 + (-2) = 3 + 2*floor(4/-10)
cmp(cmp,())&3+4/~9*2
# -4 = 1 - 5
cmp(cmp,())&3+4/~9*2-1-1-1-1-1
# -2 = (-4) | 6
cmp(cmp,())&3+4/~9*2-1-1-1-1-1|6
# -3 = (-4) | 1 = (-4) | floor(6/4) = (-4) | (6>>2)
cmp(cmp,())&3+4/~9*2-1-1-1-1-1|6<<7<<7>>8>>8
#  0 = -3 and 0
cmp(cmp,())&3+4/~9*2-1-1-1-1-1|6<<7<<7>>8>>8and 0
# +5 = -3 and 05
cmp(cmp,())&3+4/~9*2-1-1-1-1-1|6<<7<<7>>8>>8and 05
# +4 = 5 ^ 1
cmp(cmp,())&3+4/~9*2-1-1-1-1-1|6<<7<<7>>8>>8and 05^True

```

Try it online!
> 4 votes

# Answer
# Jelly, 984

```
LNḂ¡:2µ}“¢¢¢£¤¥¦©¬®½¿€ÆÇÐÑ×ØŒÞßæçðıȷñ÷øœþ !"#$%&'()*+,-./013456789;<=>?@ABCDEFGHIJKMOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|~¶°¹²³⁴⁵⁶⁷⁸⁹⁺⁻⁼⁽⁾ƁƇƊƑƓƘⱮƝƤƬƲȤɓƈɗƒɠɦƙɱɲƥʠɼʂƭʋȥẠḄḌẸḤỊḲḶṂṆỌṚṢṬỤṾẈỴẒȦĊḊĖḞĠḢİĿṀṄȮṖṘṠṪẆẊẎŻạḅḍẹḥịḳḷṃṇọṛṣṭ§Äẉỵẓȧḃċḋėḟġḣŀṁṅȯṗṙṡṫẇẋẏż”‘

```

Try it online!

You can see the prefixes (separated by a double newline) here.

The numbers printed are, in order:

```
0 1 -1 -2 2 -3 3 -4 4 -5 5 -6 6 -7 7 -8 8 -9 9 -10 10 -11 11 -12 12 -13 13 -14 14 -15 15 -16 16 -17 17 -18 18 -19 19 -20 20 -21 21 -22 22 -23 23 -24 24 -25 25 -26 26 -27 27 -28 28 -29 29 -30 30 -31 31 -32 32 -33 33 -34 34 -35 35 -36 36 -37 37 -38 38 -39 39 -40 40 -41 41 -42 42 -43 43 -44 44 -45 45 -46 46 -47 47 -48 48 -49 49 -50 50 -51 51 -52 52 -53 53 -54 54 -55 55 -56 56 -57 57 -58 58 -59 59 -60 60 -61 61 -62 62 -63 63 -64 64 -65 65 -66 66 -67 67 -68 68 -69 69 -70 70 -71 71 -72 72 -73 73 -74 74 -75 75 -76 76 -77 77 -78 78 -79 79 -80 80 -81 81 -82 82 -83 83 -84 84 -85 85 -86 86 -87 87 -88 88 -89 89 -90 90 -91 91 -92 92 -93 93 -94 94 -95 95 -96 96 -97 97 -98 98 -99 99 -100 100 -101 101 -102 102 -103 103 -104 104 -105 105 -106 106 -107 107 -108 108 -109 109 -110 110 -111 111 -112 112 -113 113 -114 114 -115 115 -116 116 -117 117 -118 118 -119 119 -120 120 -121 121 -122 122 123

```
> 4 votes

# Answer
## Batch, 176³/7744 = 704

```
@cmd/cset/a%~z0-110
: !"#$&'()*+,.23456789;<=>?ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`bfghijklnopqruvwxy{|} ¡¢£¤¥¦§¨©ª«¬®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ

```

The first prefix includes the colon and outputs the number -88. Subsequent prefixes output ascending numbers and the final program outputs 87.
> 3 votes

# Answer
# Pyth, \\$(249^{3})/15500 = 996.0\\$

```
-C\|l"\x01\x02\x03\x04\x05\x06\x07\x08\t\n\x0b\x0c\r\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19\x1a\x1b\x1c\x1d\x1e\x1f !#$%&\'()*+,./0123456789:;<=>?@ABDEFGHIJKLMNOPQRSTUVWXYZ[]^_`abcdefghijkmnopqrstuvwxyz{}~\x80\x81\x82\x83\x84\x85\x86\x87\x88\x89\x8a\x8b\x8c\x8d\x8e\x8f\x90\x91\x92\x93\x94\x95\x96\x97\x98\x99\x9a\x9b\x9c\x9d\x9e\x9f\xa0¡¢£¤¥¦§¨©ª«¬\xad®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ

```

All of the escaped characters are single bytes - I've presented the program in this form for ease of copying and pasting. This link is to the full program without escaped characters; as can be seen there are a lot of placeholders for the unprintable characters used.

The approach used is similar to lirtosiast's TI-BASIC answer, though I wrote my answer before browsing the other entries. The cord works as follows:

```
-C\|l"...
  \|        "|"
 C          Character code of the above, i.e. 124
-           Subtract from the above...
    l"...   ... the length of the trailing string - the closing quote is inferred

```

The string is made of every single-byte character other than 0 (NULL), 127 (backspace), and the boilerplate characters (`-C\|l"`). That way, each character of the string can be removed one at a time to produce strings of lengths 248 down to 0. These programs yield results in the range \[-124 - 124\], with sum of absolute values of 15500.

The code was generated using this program:

```
+J"-C\\|l\""sCM-U256+CMJ,Z127
 J"-C\\|l\""                    Assign the boilerplate code to J
                     CMJ        Get the character code of each character in J
                    +   ,Z127   Append 0 and 127
               -U256            Get values in range [0-256) which are not in the above
             CM                 Get each character with code points in the above
            s                   Concatenate into string
+J                              Prepend boilerplate

```

And the sum of the numbers generated from each of the truncated programs was found with this program:

```
sm.a.vd>._+J"-C\\|l\""sCM-U256+CMJ,Z127 5
          +J"-C\\|l\""sCM-U256+CMJ,Z127     The full program string, as above
        ._                                  Get the prefixes of the above
       >                                5   Discard the first 5 (those prefixes which don't include all the boilerplate code)
 m                                          Map each of the above to:
    .vd                                       Evaluate as Pyth code
  .a                                          Take the absolute value of the above
s                                           Take the sum

```
> 3 votes

# Answer
## Python 2, \\$11^3/53 = 25.1132075472\\$

```
015-8*2+6/3&9%7if[]else 4^ord('\b')

```

Prefixes:

```
0                                   # 0

01                                  # 1

015                                 # 13 (octal)

015-8                               # 5

015-8*2                             # -3

015-8*2+6                           # 3

015-8*2+6/3                         # -1

015-8*2+6/3&9                       # 9 (-1 bitwise-AND 9 = 9)

015-8*2+6/3&9%7                     # 2

015-8*2+6/3&9%7if[]else 4           # 4

015-8*2+6/3&9%7if[]else 4^ord('\b') # 12 (4 bitwise-XOR 8 -- OR would also work)

```

Not optimal, but the best I could personally find with this particular structure.
> 2 votes

# Answer
# Python 2 \\$6^3/9 = 24\\$

```
False-False**0&1+[[]<[[]]][[]<[]]^~3>>2

```

Here are the prefixes and what they output

```
 0 : False-False
-1 : False-False**0
 1 : False-False**0&1
 2 : False-False**0&1+[[]<[[]]][[]<[]]
-2 : False-False**0&1+[[]<[[]]][[]<[]]^~3
-3 : False-False**0&1+[[]<[[]]][[]<[]]^~3>>2

```
> 2 votes

# Answer
# Clean, 40\\$^3\\$/400 = 160

```
import StdEnv,Data.GenDefault,Gast.GenLibTest
derive genShow G
derive gDefault G
n = sum[(bitnot o bitnot) one \\ n <-: s]-one-one-one-one-one-one-one-one-one-one-one-one-one-one-one-one-one-one-one-one-one
s = (hd o show o d) undef
d :: G -> G
d g = gDefault{|*|} g
:: G = GABCFHIJKMNOPQRUVWXYZcjkqxyz_0123456789`

```

Try it online!

Defines `n` which produces `-20, -19, ..., 18, 19` depending on the length of the type `G`.

The smallest prefix of `G` looks like `:: G = G`, preceded by the assorted imports and definitions.
The largest prefix of `G` looks like `:: G = GABCFHIJKMNOPQRUVWXYZcjkqxyz_0123456789``, similarly preceded.
> 2 votes

# Answer
# Japt, \\$245^3/15006=980.0163268026123\\$

```
_Ê-122}$($"
 !#%&')*+,./03456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^`abcdefghijklmnopqrstuvwxyz|~€‚ƒ„…†‡ˆ‰Š‹ŒŽ‘’“”•–—˜™š›œžŸ ¡¢£¤¥¦§¨©ª«¬®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉËÌÍÎÏÐÑÒÓÔÕÖ×ØÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ

```

Try it online!

Like the other entries, uses the length of a string. Characters in the starting snippet, as well as `\r` (textareas don't play nice with this) and `{` (string interpolation character) are excluded from the string.

First program is `_Ê-122}$($"`, each program is one character longer with the exception of when you add `\\`.
> 2 votes

# Answer
# Python 3, \\$(6^{3})/12 = 18\\$

```
0x1-2+3|True*~4

```

This is a snippet.

The individual prefix snippets are:

```
0          # gives 0

0x1        # gives 1 (hex syntax)

0x1-2      # gives -1 (1 minus 2)

0x1-2+3    # gives 2 (-1 plus 3)

0x1-2+3|True # gives 3 (True == 1; 2 bitwise-OR 1 == 3)

0x1-2+3|True*~4 # gives -5 (~4 == -5; True*~4 == -5; 2|-5 == -5)

```

Python's bitwise operators treat negative integers as two's complement with unlimited `1`s to the right, so `-5` is treated as `...11111011`, which when ORed with `...000010` gives `...11111011` unchanged.
> 1 votes

# Answer
## Excel, \\$(6^{3})/12 = 18\\$

```
=0              0
=01             1
=01*2           2
=01*2-5         -3
=01*2-5+8       5
=01*2-5+8/4     -1

```

`Prefix` challenge does not gel well with Excel's formula structure
> 1 votes

# Answer
# Charcoal, ~~95³/2256 = 380.04211~~ 96³/2304 = 384

```
Ｉ⁻⁴⁸Ｌ´´ !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~

```

The first prefix is the first 7 bytes and outputs the number `47`. Try it online! Subsequent prefixes output descending numbers and the final program outputs `-48`. Try it online! Edit: Increased score by 3.95789 thanks to @ASCII-only.
> 1 votes

# Answer
# Runic Enchantments, 117<sup>3</sup>/3422 = 468.034

```
>"ul'B-$;	 !#%&()*+,.:0123456789@<=?ACDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijkmnopqrstvwxyz{|}~€

```

Try it online!

And the prefix.

Prints \[-58,58\] inclusive.

Uses a similar tactic as other entries, using a progressively longer string, getting its length, subtracts `B` (decimal value of `66`), and prints the result. Uses a non-printing character  (shown in the code block as  because apparently that's what `€` evaluates to in HTML) in order to utilize byte value `0x80` (and consuming an otherwise unusable `0x00`) and score one more value. Only byte values up to 127 that can't be represented in any fashion are `10` and `13`, because they would cause the program to be two lines tall and not be read correctly by the instruction pointer.
> 1 votes

---
Tags: number, code-challenge, restricted-source
---


title: Floating over the integers

text:
# Question
Title: Floating over the integers
As you may know, the typical binary floating point numbers in a computer language are quite different than the typical integer numbers in a computer language. Floating point numbers can represent a much larger range, and can represent fractional amounts, however there is a trade-off that is frequently elided.

The distance between integers is constant, and in fact the value of that constant is one. The distance between floating point numbers, however, is variable, and increases the further one travels down the number line, away from the origin at 0. At some point, that distance is so large that the floating point numbers start skipping over integers, and many integers that are technically less than the maximum value of the floating point numbers, cannot actually be represented by floating point numbers.

The challenge:

Write a program that when given the number n, will print out the first n positive integers that cannot be represented by a floating point number in your language of choice.

* "First n positive integers" means, lowest in value, closest to the origin, and distinct from each other.
* Infinite precision floating point numbers are not allowed.
* It doesn't matter whether you choose 32 bit floats, 64 bits floats, or some other type of float, as long as it is a non-infinite precision floating point number in your language of choice, on your machine of choice.
* Order of numbers does not matter
* This is Code Goﬂ. Smallest number of characters wins.
* Good luck and have fun

Example:

In Rust, using 32 bit floating point builtin type 'f32':

```
n=4, result = [16777217,16777219,16777221,16777223]

```

---

(updated - 1 order doesnt matter - 2 Golf-\>Goﬂ)

# Answer
# cQuents, 9 bytes

```
&#N_=N+.0

```

Try it online!

`&` is broken on TIO right now, so TIO link will not work, but it would time out anyway, as the only way to start at `2^53` is modifing the interpreter.

## Explanation

```
           Implicit input n
&          Output first n terms of the sequence
 #         Only include an integer N in the sequence if:
  N        N
   _=        is not equal to
     N+.0                    N converted to float

```
> 1 votes

# Answer
# Perl 6, 28 characters

```
{grep({.Num+|0-$_},^∞)[^$_]}

```

Try it online!

This is actually 30 bytes, but the challenge is scored in characters.

This should work theoretically. This creates a lazy list of numbers that compares the default number type (with arbitrary precision) against the same number converted to a `Num` datatype, which is a 64-bit floating point number, and returns the first \\$n\\$ elements of the list

Here's a version starting at \\$2^{53}-5\\$
> 3 votes

# Answer
# C (gcc), 58 bytes

```
f(n,i){for(i=9;n;i++)i-(int)(i+.0f)&&printf("%d ",i,n--);}

```

Try it online!

Works with 32-bit `float`.
> 3 votes

# Answer
# JavaScript, 46 bytes

```
n=>{for(x=1n;n;)+[++x]!=x&&console.log(x)&n--}

```

This will certainly timeout on TIO. So, here is a TIO link which initialize `x` with 253.

---

* Save ~~7~~ 10 bytes, thanks to Neil.
* Save 2 bytes, thanks to Arnauld
> 2 votes

# Answer
# Ruby 2.6, 42 bytes

```
->n{(1..).lazy.select{|i|i!=i*1.0}.take n}

```

Works with 64-bit floats, returns an enumerator.

### Ruby 2.5 and below, 43 bytes

```
->n{1.step.lazy.select{|i|i!=i*1.0}.take n}

```

And finally, the one that actually finishes in reasonable time:

```
->n{(2**53).step.lazy.select{|i|i!=i*1.0}.take n}

```

Try it online!
> 2 votes

# Answer
# Java 8, ~~68~~ 67 bytes

```
n->{for(int i=9;;)if(++i!=(int)(i+0f))System.out.println(i*n/n--);}

```

Uses the 32-bit `float`, but by changing `0f` to `0d` and `int` to `long` it can also be tested with the 64-bit `double`.

Try it online with `int` and `0f`.
Try it online with `long` and `0d`.

**Explanation:**

```
n->{                       // Method with integer parameter and no return-type
  for(int i=9;;)           //  Loop `i` from 9 upwards indefinitely:
    if(++i                 //   Increase `i` by 1 first
          !=               //   And if it does not equal:
            (int)(i+0f))   //   Itself as float, and casted back to integer:
      System.out.println(i //    Print the current `i`
        *n/n--);}          //    And decrease `n` by 1
                           //    (and due to the `n/n`, the infinite loop will stop as soon
                           //     as `n` becomes 0, with a division by zero error)

```
> 2 votes

# Answer
# Python 2, 57 bytes

```
n=1
exec"while n==int(.0+n):n+=1\nprint n;n+=1\n"*input()

```

Starting from 1 takes a very long time. For testing purposes, starting at \\$2^{53}\\$ gives the same results but much quicker: Try it online!

We count up values of `n` (an integer) until we find one for which converting to a float (by adding `.0`) and back to an int doesn't result in the same number. We then print that value and go to the next `n`. An `exec` loop lets us do this a fixed number of times according to the input.
> 1 votes

# Answer
# C# (Visual C# Interactive Compiler), 54 bytes

```
n=>{for(int i=1;;)if(++i!=(int)(i+0f))Print(i*n/n--);}

```

Port of Kevin Cruijssen's Java answer

Try it online!
> 1 votes

# Answer
# 05AB1E (legacy), 10 bytes

```
µ¾ÐtnïÊi,¼

```

No TIO, because it will time out way before it reaches the first number `9007199254740993`.. I'm using the legacy, since it is run in Python, so will output the same numbers as the Python answer. I'll see if I can determine the first few numbers for the new version of 05AB1E as well, which is run in Elixir (but that will be a separated answer in that case).

As alternative for the TIO, here a prove that `tnï` for input `9007199254740993` does not result in `9007199254740993`, but in `9007199254740994` instead: Try it online.

**Explanation:**

```
µ           # Loop until the counter_variable is equal to the (implicit) input
            # (the counter_variable is 0 by default)
 ¾Ð         #  Push the counter_variable three times
   t        #  Take its square-root
    n       #  And then the square of that
     ï      #  And cast it back from a decimal to an integer
      Êi    #  If they are NOT equal:
        ,   #   Print the counter_variable
         ¼  #   And increase the counter_variable by 1

```

05AB1E has no builtin to set the `counter_variable` manually unfortunately, otherwise I would have set it to about `9007199254740000` at the start.
> 1 votes

---
Tags: code-golf, integer, floating-point
---