A023103 (10^n)-th digit of infinite string 12345678910111213141516...

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, 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, 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

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• base

Comments

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.]

References

• Lucio Artiaga and Lloyd D. Davis, Algorithms and Their Computer Solutions, Merrill, 1972, p. 160.
• M. Kraitchik, Mathematical Recreations. Dover, NY, 2nd ed., 1953, p. 49.

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..1000
• Sean A. Irvine, Java program (github)

Crossrefs

10^n-th digit in the almost natural number (A007376).

Cf. Champernowne constant or Mahler's number A033307.

Cf. A033713.

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[10^#, 10] &, 105, 0] (* modified by Robert G. Wilson v, Jul 15 2014 *)

Extensions

Edited by Robert G. Wilson v, Jun 18 2002