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.

A066023 (a(n)^7+1)/(n^7+1) is the smallest integer > 1.

Original entry on oeis.org

3, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 46656, 50653, 54872, 59319, 64000
Offset: 1

Views

Author

Robert G. Wilson v, Dec 11 2001

Keywords

Links

Crossrefs

Cf. A065964.

Programs

  • Mathematica
    Do[k = 1; While[m = (k^7 + 1)/(n^7 + 1); m < 2 || !IntegerQ[m], k++ ]; Print[k], {n, 1, 40} ]
  • PARI
    { for (n=1, 200, f=n^7 + 1; a=n + 1; while (frac((a^7 + 1)/f) !=0, a++); write("b066023.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 07 2009

Formula

Conjecture: a(n) = A000578(n), n>1. - R. J. Mathar, Aug 28 2014
Empirical g.f.: x*(2*x^4-8*x^3+13*x^2-4*x+3) / (x-1)^4. - Colin Barker, Aug 28 2014

A066018 a(n) is the smallest k such that (k^4 + 1)/(n^4 + 1) is an integer > 1.

Original entry on oeis.org

3, 8, 27, 64, 125, 216, 343, 474, 43, 781, 1331, 1728, 2197, 1807, 3375, 4096, 4913, 1600, 807, 8000, 9261, 10648, 12167, 13824, 7353, 17576, 6721, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 46656, 50653, 4015, 59319, 20723
Offset: 1

Views

Author

Robert G. Wilson v, Dec 11 2001

Keywords

Links

Crossrefs

Cf. A065964.

Programs

  • Mathematica
    Do[k = 1; While[m = (k^4 + 1)/(n^4 + 1); m < 2 || !IntegerQ[m], k++ ]; Print[k], {n, 1, 40} ]
  • PARI
    { for (n=1, 250, f=n^4 + 1; a=n + 1; while (frac((a^4 + 1)/f) !=0, a++); write("b066018.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 06 2009

A066020 a(n) is the smallest k such that (k^5 + 1)/(n^5 + 1) is an integer > 1.

Original entry on oeis.org

3, 8, 27, 64, 125, 118, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 11663, 19683, 21952, 11189, 27000, 29791, 32768, 35937, 39304, 42875, 46656, 50653, 54872, 59319, 64000
Offset: 1

Views

Author

Robert G. Wilson v, Dec 11 2001

Keywords

Links

Crossrefs

Cf. A065964.

Programs

  • Mathematica
    Do[k = 1; While[m = (k^5 + 1)/(n^5 + 1); m < 2 || !IntegerQ[m], k++ ]; Print[k], {n, 1, 40} ]
  • PARI
    { for (n=1, 200, f=n^5 + 1; a=n + 1; while (frac((a^5 + 1)/f) !=0, a++); write("b066020.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 06 2009

A066021 (a(n)^6+1)/(n^6+1) is the smallest integer > 1.

Original entry on oeis.org

3, 7, 27, 64, 125, 119, 343, 177, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 46656, 50653, 54872, 59319, 64000
Offset: 1

Views

Author

Robert G. Wilson v, Dec 11 2001

Keywords

Crossrefs

Cf. A065964, A098239.

Programs

  • Mathematica
    Do[k = 1; While[m = (k^6 + 1)/(n^6 + 1); m < 2 || !IntegerQ[m], k++ ]; Print[k], {n, 1, 40} ]
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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