cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

0, 7, 81, 283, 684, 1318, 8792, 15975, 61274, 314072, 4057579
Offset: 1

Views

Author

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

Keywords

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

A173550 a(n) = k smallest exponent of N = 2^k of first prime(1) = 2 where string "p(1) ... p(n)" appears in the decimal representation of N (n=1,2,...).

Original entry on oeis.org

1, 41, 81, 256, 2810, 19680, 131516, 1812049
Offset: 1

Views

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Feb 21 2010

Keywords

Examples

			n=1: 2^1 = 2
n=2: 2^41 = 2199023255552, "23" appears on decimals 6-7
n=3: 2^81 = 2417851639229258349412352, "235" appears on decimals 22-24
n=4: 2^256 has 78 decimals, "2357" appears on decimals 20-23
2^256 = 115792089237316195423570985008687907853269984665640564039457584007913129639936

References

  • Julian Havil, Impossible?: Surprising Solutions to Counterintuitive Conundrums, Princeton University Press 2008

Crossrefs

Cf. A000079, A018802, A171132, A171242, A171489, A171652, A171768

Extensions

Extended and edited by Hans Havermann, Mar 20 2010
Showing 1-2 of 2 results.

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