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

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

Author

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

Keywords

• nonn
• hard
• more

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

• J. Brillhart, Concerning the number 2^(2p)+1, p prime, Math. Comp. 16 (80) (1962) 424-430.
• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
• S. S. Wagstaff, Jr., The Cunningham Project

Crossrefs

Cf. A006598.

Programs

PARI

is(n)=isprime(2^n-2^((n+1)/2)+1) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(16)-a(18) from Robert G. Wilson v, Sep 07 2000

a(19)-a(23) from Serge Batalov, Jun 16 2020