%I #18 Dec 01 2014 00:21:46
%S 1,2,4,8,1,2,3,6,1,0,3,1,0,2,7,6,5,4,0,9,1,4,7,1,5,5,7,0,2,5,1,5,5,5,
%T 0,4,8,1,9,0,2,2,1,0,5,6,8,1,9,1,8,2,3,5,4,4,4,3,8,7,0,0,6,3,1,2,1,5,
%U 5,0,1,1,5,9,9,3,0,1,6,4,9,1,2,5,1,8,4,3,1,1,7,2,5,7,9,6,6,7,4,9,7,1,7,0,0,3,5,0
%N (2^n)-th digit of infinite string 12345678910111213141516...
%F a(n) = A007376(2^n). - _Robert Israel_, Jun 27 2014
%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[2^#, 10] &, 105, 0] (* _Robert G. Wilson v_, Jun 27 2014 and modified Jul 15 2014 *)
%Y Cf. A007376, A033307, A023103.
%K nonn,base
%O 0,2
%A _David W. Wilson_