A171768 a(n) = smallest exponent k such that the string "1 2 ... n" appears in the decimal expansion of 2^k.

0, 7, 81, 283, 684, 1318, 8792, 15975, 61274, 314072, 4057579

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Dec 18 2009

Keywords

• nonn
• base

Comments

The first time "0" appears is in a(10). - Robert G. Wilson v, Feb 26 2013

Examples

			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.
		

References

• Julian Havil, Impossible?: Surprising Solutions to Counterintuitive Conundrums, Princeton University Press 2008
• Ross Honsberger, Ingenuity in mathematics, Random House/Singer School Division 1970

Crossrefs

Cf. A000079, A018802, A171132, A171242, A171489, A171652.

Programs

Mathematica

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 *)

Extensions

a(6)-a(10) from Robert G. Wilson v, Feb 26 2013

a(11) from Giovanni Resta, Feb 26 2013