A007671 Numbers n such that 2^n + 2^((n + 1)/2) + 1 is prime.

1, 3, 5, 11, 19, 29, 157, 163, 283, 379, 997, 10141, 14699, 77291, 85237, 106693, 203789, 3704053

Offset: 1

Author

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

Keywords

• nonn
• hard
• more

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 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. A057429.

Programs

PARI

for(n=1, 2000, if(n%2==1&&ispseudoprime(2^n+2^((n+1)/2)+1), print1(n,","))) \\ Charles R Greathouse IV, Feb 17 2017 edited by Aurelien Gibier Jun 29 2024.

Extensions

More terms from Robert G. Wilson v, Sep 07 2000

203789 found and proved prime by Mike Oakes, on Sep 28 2000.

a(18) from Serge Batalov, Jun 16 2020