A125743 Primes p such that (3^p - 3^((p + 1)/2) + 1)/7 is prime.

5, 31, 53, 163, 509, 1061, 13627, 20047, 28411, 50993, 71453, 272141, 1353449

Offset: 1

Author

Alexander Adamchuk, Dec 04 2006

Keywords

• hard
• more
• nonn

Comments

PrimePi[ a(n) ] = {3, 11, 16, 38, 97, 178,...}.

Links

• Henri & Renaud Lifchitz, PRP Records.

Crossrefs

Cf. A125744 = 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,1,178}]

Extensions

a(6)-a(11) from Lelio R Paula (lelio(AT)sknet.com.br), May 08 2008

a(12) from Serge Batalov, Mar 07 2014

a(13) from Serge Batalov, Mar 25 2014