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A023103
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(10^n)-th digit of infinite string 12345678910111213141516...
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3
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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
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OFFSET
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0,3
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COMMENTS
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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.]
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REFERENCES
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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.
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LINKS
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MATHEMATICA
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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 *)
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CROSSREFS
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10^n-th digit in the almost natural number (A007376).
Cf. Champernowne constant or Mahler's number A033307.
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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