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.

A126893 Numbers k such that k^6 + 82991 is prime.

Original entry on oeis.org

7980, 8526, 11676, 18774, 26754, 31584, 34314, 34650, 43134, 51576, 64176, 65184, 65730, 65856, 70224, 71190, 71316, 76650, 78834, 79506, 81564, 84294, 91266, 92904, 96096, 96894, 105294, 110376, 111090, 113484, 117684, 118146, 118566
Offset: 1

Views

Author

Artur Jasinski, Dec 31 2006

Keywords

References

  • Ribenboim P., 1996. The Little Book of Big Primes. Springer Verlag.

Crossrefs

Cf. A066386, A126894, A126895.

Programs

  • Magma
    [n: n in [0..200] | IsPrime(n^6+82991)] // Vincenzo Librandi, Nov 23 2010
  • Mathematica
    a = {}; Do[If[PrimeQ[x^6 + 82991], AppendTo[a, x]], {x, 7978, 40000}]; a
Select[ Range@119000, PrimeQ[#^6 + 82991] &] (* Robert G. Wilson v, Jan 21 2018 *)
  • PARI
    is(n)=isprime(n^6+82991) \\ Charles R Greathouse IV, Feb 17 2017

A126895 Numbers n such that (1365n)^12+4094 is prime.

Original entry on oeis.org

125, 133, 171, 359, 361, 405, 433, 471, 649, 675, 925, 995, 1085, 1277, 1281, 1393, 1487, 1511, 1519, 1553, 1607, 1687, 1855, 2023, 2025, 2031, 2207, 2259, 2387, 2495, 2673, 2749, 2851, 2957, 3057, 3067, 3251, 3271, 3277, 3355, 3401, 3599, 3701, 3763
Offset: 1

Views

Author

Artur Jasinski, Dec 31 2006

Keywords

Comments

A126894(n)/1365

References

  • Ribenboim P., 1996. The Little Book of Big Primes. Springer Verlag.

Crossrefs

Cf. A066386, A126893, A126894.

Programs

A122131 Numbers n such that n^12 + 488669 is prime.

Original entry on oeis.org

616980, 764400, 933660, 1051050, 1730820, 1758120, 2467920, 3093090, 3164070, 3461640, 3696420, 3890250, 3923010, 3950310, 4051320, 4075890, 4196010, 4286100, 4324320, 4337970, 4389840, 4556370, 4561830, 4720170, 4793880
Offset: 1

Views

Author

Eric W. Weisstein, Aug 21 2006

Keywords

Comments

When n is odd the polynomial produces even values, so it is trivially composite. When n ends in 2, 4, 6, or 8 then n^12 ends in 6, so the polynomial produces values ending in 5, again composite. Hence all the values in this sequence are divisible by 10. - Dmitry Kamenetsky, Nov 08 2016
By Fermat's Little Theorem the polynomial is divisible by 2, 3, 5, 7 and 13 when n is not divisible by these primes. Hence all the values in the sequence are divisible by the product of these primes, 2730. - Chun Lok Yiu, Mar 14 2022

References

  • Paulo Ribenboim, The Little Book of Big Primes, Springer Verlag, 1996.

Links

Crossrefs

Cf. A066386, A126893, A126894, A126897.

Programs

  • Magma
    [n: n in [0..10^7] | IsPrime(n^12+488669)]; // Vincenzo Librandi, May 03 2014
  • Mathematica
    a = {}; Do[If[PrimeQ[x^12 + 488669], AppendTo[a, x]], {x, 616979, 10000000}]; a (* Artur Jasinski, Dec 31 2006 *)
Select[Range[10^7], PrimeQ[#^12 + 488669] &] (* Vincenzo Librandi, May 03 2014 *)
  • PARI
    is(n)=isprime(n^12+488669) \\ Charles R Greathouse IV, Jun 06 2017

Extensions

Edited by N. J. A. Sloane, May 07 2007

A126897 Numbers n such that (2730n)^12+488669 is prime.

Original entry on oeis.org

226, 280, 342, 385, 634, 644, 904, 1133, 1159, 1268, 1354, 1425, 1437, 1447, 1484, 1493, 1537, 1570, 1584, 1589, 1608, 1669, 1671, 1729, 1756, 1779, 2221, 2399, 2424, 2462, 2501, 2544, 2829, 2831, 2871, 2938, 2944, 3037, 3070, 3184, 3208, 3254, 3256
Offset: 1

Views

Author

Artur Jasinski, Dec 31 2006

Keywords

Comments

A122131(n)/2730

References

  • Ribenboim P., 1996. The Little Book of Big Primes. Springer Verlag.

Crossrefs

Cf. A066386, A126893, A126894, A126895, A122131.

Programs

Showing 1-4 of 4 results.

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

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