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Allen, DP (1999)

A new approach to the first digit phenomenon

The Toth-Maatian Review 14(3), pp. 6839-6847.


Abstract: In this paper, we first show by extending the proof of B. J. Flehenger [1] that the integers represented to the base ten also have the first digit property. We note tat R. E. Whitney [2] has also proven this using the logarithmic matrix method of summability. We then abstract from these two proofs in view of the Peano Axioms to obtain a (new) definition of of what it means to sum a sequence in the spirit of the Peano Axioms for the positive integers (which includes Flehinger's and Whitney's methods as special cases) and conjecture any method of summation of this very general type assigns the limit log((A+1)/A) to the two sequences s(n) and t(n) where (a) s(n) = 1 if n has first digit equal to A else zero, and (b) t(n) = 1 if the n-th prime has first digit A else zero. The conjecture, if true, yields new explanation of the first digit phenomenon by reducing it to the its first cause: the well ordering of the positive integers.

@article {, AUTHOR = {Dennis P. Allen}, TITLE = {A new approach to the first digit phenomenon}, JOURNAL = {The Toth-Maatian Review}, YEAR = {1999}, VOLUME = {14}, NUMBER = {3}, PAGES = {6839--6847}, URL = {}, }

Reference Type: Journal Article

Subject Area(s): Number Theory, Probability Theory