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.

A007670 Numbers n such that 2^n - 2^((n + 1)/2) + 1 is prime.

Original entry on oeis.org

3, 7, 47, 73, 79, 113, 151, 167, 239, 241, 353, 367, 457, 1367, 3041, 27529, 49207, 160423, 364289, 991961, 1203793, 1667321, 4792057
Offset: 1

Views

Author

N. J. A. Sloane, Robert G. Wilson v

Keywords

Comments

If A007670 is a proper subset of A057429, then 364289 & 991961 are the next two terms.

References

  • J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A006598.

Programs

Extensions

a(16)-a(18) from Robert G. Wilson v, Sep 07 2000
a(19)-a(23) from Serge Batalov, Jun 16 2020

A100014 Least a(n) such that a(n)*2^n*(2^n-1)+1 is prime.

Original entry on oeis.org

1, 1, 2, 1, 6, 3, 5, 12, 3, 5, 8, 6, 5, 3, 18, 8, 41, 5, 11, 14, 66, 8, 2, 9, 18, 8, 21, 12, 30, 16, 6, 1, 6, 8, 33, 2, 53, 23, 2, 5, 21, 15, 6, 12, 20, 5, 5, 28, 53, 80, 11, 53, 9, 5, 56, 2, 120, 5, 23, 16, 9, 8, 5, 9, 24, 25, 62, 131, 41, 51, 12, 3, 99, 56, 2, 37, 155, 3, 23, 55, 29, 9, 2, 33
Offset: 1

Views

Author

Pierre CAMI, Nov 18 2004

Keywords

Comments

Numbers n such that a(n)=2 are found in A006598. - Michel Marcus, Mar 07 2013

Examples

			1*2^5*(2^5-1)+1=993=3*331
2*2^5*(2^5-1)+1=1985=5*397
3*2^5*(2^5-1)+1=2977=13*229
4*2^5*(2^5-1)+1=3969=3*1323
5*2^5*(2^5-1)+1=4961=11*451
6*2^5*(2^5-1)+1=5953 prime so a(5)=6

Programs

  • PARI
    a(n) = {k = 1; while (! isprime(k*2^n*(2^n-1) + 1), k++); return (k);} \\ Michel Marcus, Mar 07 2013

A325914 Primes of the form (2^k-1)*2^(k+1)+1.

Original entry on oeis.org

5, 113, 140737471578113, 9444732965601851473921, 604462909806215075725313, 10384593717069655112945804582584321, 2854495385411919762116496381035264358442074113, 187072209578355573530071639244871112681892570202113
Offset: 1

Views

Author

Gary Wright, Sep 08 2019

Keywords

Comments

The next two terms are 883423532389192164791648750371459256584513952652893606156996040365965313
and 3533694129556768659166595001485837028996511802181406170435598282024550401. - N. J. A. Sloane, Sep 13 2019

Crossrefs

These are the primes in A092440. See A006598 for the values of k.

Extensions

Edited by N. J. A. Sloane, Sep 13 2019
Showing 1-3 of 3 results.

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

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