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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 (list; graph; refs; listen; history; text; internal format)
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^p-3^((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

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Last modified September 25 17:21 EDT 2020. Contains 337344 sequences. (Running on oeis4.)