

A007670


Numbers n such that 2^n  2^((n + 1)/2) + 1 is prime.
(Formerly M2703)


8



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

1,1


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

Table of n, a(n) for n=1..23.
J. Brillhart, Concerning the number 2^(2p)+1, p prime, Math. Comp. 16 (80) (1962) 424430.
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


PROG

(PARI) is(n)=isprime(2^n2^((n+1)/2)+1) \\ Charles R Greathouse IV, Feb 17 2017


CROSSREFS

Cf. A006598.
Sequence in context: A231893 A132565 A129518 * A263806 A074714 A064457
Adjacent sequences: A007667 A007668 A007669 * A007671 A007672 A007673


KEYWORD

nonn,hard,more


AUTHOR

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


EXTENSIONS

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


STATUS

approved



