A023104 (2^n)-th digit of infinite string 12345678910111213141516...

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, 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, 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

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• base

Crossrefs

Cf. A007376, A033307, A023103.

Programs

Mathematica

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 *)

Formula

a(n) = A007376(2^n). - Robert Israel, Jun 27 2014