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

0,3

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)

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 *)

Crossrefs

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

Cf. Champernowne constant or Mahler's number A033307.

Cf. A033713.

Sequence in context: A065169 A247617 A099217 * A153454 A198877 A201752

Adjacent sequences: A023100 A023101 A023102 * A023104 A023105 A023106

Keyword

nonn,base

Author

David W. Wilson

Extensions

Edited by Robert G. Wilson v, Jun 18 2002

Status

approved