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.

Showing 1-4 of 4 results.

A171652 The initial decimal digits of 2^a(n) are the decimal digits of n followed by n.

Original entry on oeis.org

50, 51, 25, 145, 142, 119, 86, 239, 93, 1558, 1598, 761, 1183, 6651, 5515, 4183, 34, 8990, 1343, 4180, 7987, 10628, 938, 5519, 4177, 10213, 10326, 6652, 1327, 5516, 12326, 4184, 11964, 6928, 6649, 8991, 653, 10373, 11549, 4181, 3706, 7988, 5862, 10629, 8988, 939, 13084
Offset: 1

Views

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Dec 14 2009

Keywords

Examples

			a(1) = 50; 2^50 = 1125899906842624
a(2) = 51; 2^51 = 2251799813685248
a(3) = 25; 2^25 = 33554432
a(10) = 1558; 2^1558 = 10109583053...744

References

  • E.I. Ignatjew, Mathematische Spielereien, Urania Verlag Leipzig-Jena-Berlin, 2. Auflage 1982

Crossrefs

Cf. A018802, A171132, A171242, A171489, A171617

Programs

  • PARI
    double(n,k)=n\=10^(#Str(n)-2*k);if(n%10^k==n\=10^k,n)
a(n)=my(s=#Str(n));for(k=1,1e6,if(double(1<

Extensions

More terms, program, and editing by Charles R Greathouse IV, Aug 02 2010

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

A171617 a(n)=k is the smallest exponent of N=2^k of first prime(1)=2 where at least 5 equal decimal digits "n n n n n" appear in the decimal representation of N (n=0,1,...9).

Original entry on oeis.org

1491, 485, 314, 221, 315, 973, 220, 317, 316, 422
Offset: 0

Views

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Dec 13 2009

Keywords

Comments

If we change the definition to allow for not just the digits but for the numbers, say "10" then this sequence can be extended. a(10) would become 263528 and a(11) would equal 165742. - Robert G. Wilson v, Oct 13 2012

Examples

			0: 2^1491: 449 decimal digits, "00000" appears on decimals 397 - 401.
1: 2^485: 146 decimal digits, "11111" appears on decimals 22 - 26.
2: 2^314: 95 decimal digits, "22222" appears on decimals 64 - 68.
3: 2^221: 67 decimal digits, "33333" appears on decimals 7 - 11.
4: 2^315: 95 decimal digits, "44444" appears on decimals 64 - 68.
5: 2^973: 293 decimal digits, "555555" (6 "5's") appears on decimals 230 - 25.
6: 2^220: 67 decimal digits, "66666" appears on decimals 7 - 11.
7: 2^317: 96 decimal digits, "77777" appears on decimals 65 - 69.
8: 2^316: 96 decimal digits, "88888" appears on decimals 65 - 69.
9: 2^422: 128 decimal digits, "99999" appears on decimals 83 - 87.

References

  • E. J. Burr, American Mathematical Monthly (December 1963, 70(10), pp. 1101-2
  • 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.

Programs

  • Mathematica
    f[n_] := Block[{k = 1, m = IntegerString[n]}, mm = m <> m <> m <> m <> m; While[ StringPosition[ ToString[2^k], mm] == {}, k++]; k]; Array[f, 10, 0] (* Robert G. Wilson v, Oct 13 2012 *)

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 1-4 of 4 results.

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