

A125738


Primes p such that 3^p  3^((p + 1)/2) + 1 is prime.


3



3, 11, 193, 239, 659, 709, 1103, 2029, 9049, 10453, 255361, 534827
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OFFSET

1,1


COMMENTS

PrimePi[ a(n) ] = {2, 5, 44, 52, 120, 127, 185, 308, 1125, 1278 ...}, the indices of the primes p.
a(13) > 1900000.  Serge Batalov, Mar 24 2014


LINKS

Table of n, a(n) for n=1..12.
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.


MATHEMATICA

Do[p=Prime[n]; f=3^p3^((p+1)/2)+1; If[PrimeQ[f], Print[{n, p}]], {n, 1, 200}]


CROSSREFS

Cf. A125739 = Primes p such that 3^p + 3^((p + 1)/2) + 1 is prime.
Cf. A007670 = Numbers n such that 2^n  2^((n + 1)/2) + 1 is prime.
Cf. A007671 = Numbers n such that 2^n + 2^((n + 1)/2) + 1 is prime.
Cf. A066408 = Numbers n such that the Eisenstein integer has prime norm.
Sequence in context: A103836 A284704 A081484 * A334176 A332771 A092840
Adjacent sequences: A125735 A125736 A125737 * A125739 A125740 A125741


KEYWORD

hard,more,nonn


AUTHOR

Alexander Adamchuk, Dec 02 2006


EXTENSIONS

More terms from A066408 by Serge Batalov, Mar 24 2014


STATUS

approved



