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%I #32 May 26 2019 02:11:49
%S 1,1,5,3,7,2,1,7,8,1,1,0,1,5,7,2,6,4,3,5,3,5,4,9,6,2,4,8,7,1,1,3,7,2,
%T 3,0,8,5,3,8,2,7,6,7,9,9,2,7,0,1,6,2,0,4,1,3,8,5,3,3,3,5,0,0,1,1,5,6,
%U 1,6,2,4,3,7,5,6,8,5,3,6,8,8,2,2,0,3,9,1,8,9,2,1,1,9,6,4,4,0,2,6,4,1,0,1,4,2,8,4
%N (10^n)-th digit of infinite string 12345678910111213141516...
%C In one of Ross Honsberger's "Mathematical Gems" series (Dolciani Mathematical Expositions, Mathematical Association of America) there is a formula for extracting the n-th digit. Would someone submit it? [Robert Wilson notes that the Mathematica program below implements this formula.]
%D Lucio Artiaga and Lloyd D. Davis, Algorithms and Their Computer Solutions, Merrill, 1972, p. 160.
%D M. Kraitchik, Mathematical Recreations. Dover, NY, 2nd ed., 1953, p. 49.
%H Robert G. Wilson v, <a href="/A023103/b023103.txt">Table of n, a(n) for n = 0..1000</a>
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a023/A023103.java">Java program</a> (github)
%t almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; Array[ almostNatural[10^#, 10] &, 105, 0] (* modified by _Robert G. Wilson v_, Jul 15 2014 *)
%Y 10^n-th digit in the almost natural number (A007376).
%Y Cf. Champernowne constant or Mahler's number A033307.
%Y Cf. A033713.
%K nonn,base
%O 0,3
%A _David W. Wilson_
%E Edited by _Robert G. Wilson v_, Jun 18 2002
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