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 1-3 of 3 results.

A144232 Prime numbers of the form 4^k +- 3.

Original entry on oeis.org

7, 13, 19, 61, 67, 1021, 4093, 4099, 16381, 65539, 262147, 1048573, 4194301, 16777213, 268435459, 1073741827, 19342813113834066795298819, 19807040628566084398385987581, 83076749736557242056487941267521533, 5316911983139663491615228241121378301, 1427247692705959881058285969449495136382746621
Offset: 1

Views

Author

Reikku Kulon, Sep 15 2008

Keywords

Links

Crossrefs

Subset of A122834.
Cf. A000040, A000668, A144231.

Programs

  • Mathematica
    Select[Flatten[Table[4^n+{3,-3},{n,100}]],PrimeQ]//Union (* Harvey P. Dale, Nov 13 2020 *)

Extensions

a(20)-a(21) from Amiram Eldar, Jul 24 2025

A107360 Numbers p (necessarily prime) such that 2^p - 1 is a Mersenne prime and (2^p+1)/3 is a Wagstaff prime.

Original entry on oeis.org

3, 5, 7, 13, 17, 19, 31, 61, 127
Offset: 1

Views

Author

Lekraj Beedassy, May 23 2005

Keywords

Comments

Intersection of A000043 and A000978.
'The New Mersenne Conjecture' (Bateman-Selfridge-Wagstaff) states that if two of the following statements about an odd positive integer p are true, then the third one is also true: (a) p = 2^k +- 1 or p = 4^k +- 3, (b) 2^p - 1 is prime, (c) (2^p + 1)/3 is prime. (Amer Math Monthly, 96 (1989) p. 125.) - R. K. Guy, May 20 2005
The next term, if it exists, is not any currently known Mersenne prime exponent or Wagstaff prime exponent: it must be larger than A000043(48) = 57885161 and cannot be 74207281, 77232917, or 82589933. See Caldwell and both Wanless links. The New Mersenne Conjecture would require this sequence to be a subsequence of A122834, in which case the next term could not be less than A122834(28) = 2305843009213693951. See Caldwell and Höglund links. - Gord Palameta, Jun 28 2019, Jun 29 2024
p either has the form 2^k -+ 1 or the form 4^k -+ 3, according to the New Mersenne Conjecture. - Lekraj Beedassy, Sep 20 2006
Primes p such that (4^p - 1)/3 is a semiprime. - Arkadiusz Wesolowski, Jun 01 2013
Numbers m != 4 such that (4^m - 1)/3 is a semiprime. - Thomas Ordowski, Sep 25 2015
The indices of Wagstaff primes relating to the new Mersenne conjecture A122834 in a list of Jacobsthal numbers A001045. - Steve Homewood, Dec 01 2020

References

  • Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 83.

Links

Crossrefs

Cf. A000043, A000978, A122834.

Programs

  • Magma
    [p: p in PrimesUpTo(500) | IsPrime(2^p-1) and IsPrime((2^p+1) div 3)]; // Vincenzo Librandi, Sep 25 2015
  • Mathematica
    Select[Prime@Range[31], PrimeQ[(2^# + 1)/3] && PrimeQ[2^# - 1] &] (* Arkadiusz Wesolowski, Jun 01 2013 *)
  • PARI
    forprime(p=2, 1e3, if (!((2^p+1) % 3) && isprime((2^p+1)/3) && isprime(2^p-1), print1(p, ", "))); \\ Altug Alkan, Sep 25 2015

A120334 Odd primes of the form p = 2^k +- 1 or p = 4^k +- 3 or such that 2^p - 1 is prime or (2^p + 1)/3 is prime or PRP.

Original entry on oeis.org

3, 5, 7, 11, 13, 17, 19, 23, 31, 43, 61, 67, 79, 89, 101, 107, 127, 167, 191, 199, 257, 313, 347, 521, 607, 701, 1021, 1279, 1709, 2203, 2281, 2617, 3217, 3539, 4093, 4099, 4253, 4423, 5807, 8191, 9689, 9941
Offset: 1

Views

Author

Jorge Coveiro, Sep 11 2007

Keywords

Comments

Odd primes satisfying at least one of the criteria considered in the New Mersenne Prime Conjecture (cf. link).

Links

Crossrefs

Supersequence of A000978, A122834.
Almost a supersequence of A000043 (excluding only A000043(1) = 2).
Showing 1-3 of 3 results.

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

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