A125738 - OEIS

A125738

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

3, 11, 193, 239, 659, 709, 1103, 2029, 9049, 10453, 255361, 534827, 2888387

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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(14) > 4400000. - Serge Batalov, Jun 20 2023

LINKS

J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

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.

KEYWORD

hard,more,nonn

AUTHOR

EXTENSIONS

More terms from A066408 by Serge Batalov, Mar 24 2014

a(13) from Ryan Propper and Serge Batalov, Jun 20 2023

STATUS

approved