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A171768
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a(n) = smallest exponent k such that the string "1 2 ... n" appears in the decimal expansion of 2^k.
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2
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0, 7, 81, 283, 684, 1318, 8792, 15975, 61274, 314072, 4057579
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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Julian Havil, Impossible?: Surprising Solutions to Counterintuitive Conundrums, Princeton University Press 2008
Ross Honsberger, Ingenuity in mathematics, Random House/Singer School Division 1970
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LINKS
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EXAMPLE
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n=1: 2^0 = 1
n=2: 2^7 = 128
n=3: 2^81 = 2417851639229258349412352
n=4: 2^283 has 86 decimals, "1234" appears on decimals 68 - 71:
2^283=
15541351137805832567355695254588151253139254712417116170014499277911234281641667985408
n=5: 2^684 has 206 decimals, "12345" appears on decimals 99 - 103.
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MATHEMATICA
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g[n_] := Block[{c = 0, k = 1}, While[k <= n, c = 10^Floor[1 + Log10[k]] c + k; k++]; c] (* from A007908 *); f[n_] := Block[{k = 0, s = ToString[g[n]]}, While[ StringPosition[ ToString[ 2^k], s] == {}, k++]; k]; Array[f, 10] (* Robert G. Wilson v, Feb 26 2013 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Dec 18 2009
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EXTENSIONS
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STATUS
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approved
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