A006599 Numbers k such that 2^(2k+1) + 2^(k+1) + 1 is prime. (Formerly M1358)

0, 1, 2, 5, 9, 14, 78, 81, 141, 189, 498, 5070, 7349, 38645, 42618, 53346

Offset

1,3

Comments

Some of the larger entries may only correspond to probable primes.

Next term >= 10^4. - Jeppe Stig Nielsen, Mar 28 2014

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

Table of n, a(n) for n=1..16.

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

Formula

a(n) = A108062(n) - 1. - Michael S. Branicky, Jan 02 2025

Prog

(PARI) isok(n) = isprime(2^(2*n+1) + 2^(n+1) + 1); \\ Michel Marcus, Mar 28 2014

Crossrefs

A108062 is essentially the same sequence.

Sequence in context: A048071 A320996 A051892 * A013933 A101201 A184535

Adjacent sequences: A006596 A006597 A006598 * A006600 A006601 A006602

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

More terms from Rick L. Shepherd, Sep 07 2002

a(13) from Jeppe Stig Nielsen, Mar 28 2014

a(14)-a(16) from Michael S. Branicky, Jan 02 2025

Status

approved