A111974 Primes of the form 2*3^k + 1.

3, 7, 19, 163, 487, 1459, 39367, 86093443, 258280327, 411782264189299, 116299474006080119380780339, 3140085798164163223281069127, 84782316550432407028588866403, 20602102921755074907947094535687, 1910009901593650473786381403548828023839870277948686259673707683

Offset: 1

Author

T. D. Noe, Aug 24 2005

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..23
• Hartosh Singh Bal and Gaurav Bhatnagar, Prime number conjectures from the Shapiro class structure, arXiv:1903.09619 [math.NT], 2019-2020.

Crossrefs

Cf. A003306 (k such that 2*3^k + 1 is prime), A003307 (k such that 2*3^k - 1 is prime), A052919.

Programs

Mathematica

Select[2*3^Range[100]+1, PrimeQ]

Formula

a(n) = A052919(A003306(n)+1). - Amiram Eldar, Jul 18 2025

Extensions

a(15) from Amiram Eldar, Jul 18 2025