A125744 Primes p such that (3^p + 3^((p + 1)/2) + 1)/7 is prime.

11, 37, 47, 97, 167, 877, 2027, 2293, 3011, 6803, 8423, 50221, 152809, 505823

Offset: 1

Author

Alexander Adamchuk, Dec 04 2006

Keywords

• hard
• more
• nonn

Comments

PrimePi[ a(n) ] = {5, 12, 15, 25, 39, 151, 307, 341, ...}.

Links

• Henri & Renaud Lifchitz, PRP Records.

Crossrefs

Cf. A125743 = Primes p such that (3^p - 3^((p + 1)/2) + 1)/7 is prime. Cf. A125738 = Primes p such that 3^p - 3^((p + 1)/2) + 1 is prime. Cf. A125739 = Primes p such that 3^p + 3^((p + 1)/2) + 1 is prime. Cf. A007670, A007671, A124165, A125742.

Programs

Mathematica

Do[p=Prime[n];f=(3^p+3^((p+1)/2)+1)/7;If[PrimeQ[f],Print[{n,p}]],{n,1,341}]

Extensions

a(9)-a(12) from Lelio R Paula (lelio(AT)sknet.com.br), May 09 2008

a(13)-a(14) from Serge Batalov, Mar 07 2014