A051646 Primes of the form 30*p + 1 where p is also prime.

61, 151, 211, 331, 571, 691, 1231, 1291, 1831, 2011, 2131, 2371, 2671, 3271, 3391, 3931, 4111, 5011, 5431, 5791, 6691, 6871, 6991, 8311, 8431, 9391, 9511, 9931, 10111, 10771, 11491, 13171, 13291, 13711, 13831, 14011, 14731, 15091, 15271, 16231, 16411, 17791, 17971

Offset: 1

Author

Labos Elemer

Keywords

• nonn
• easy

Comments

Analogous to A005385, safe primes. Can be called 30-safe primes.

Examples

			61 is in the sequence because both 2 and 30*2 + 1 = 61 are primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005384, A005385, A007693, A051645, A128470.

Programs

Mathematica

Select[30 * Prime[Range[120]] + 1, PrimeQ] (* Amiram Eldar, Feb 24 2025 *)

PARI

isok(k) = isprime(k) && k % 30 == 1 && isprime((k-1)/30); \\ Amiram Eldar, Feb 24 2025

Formula

a(n) = A128470(A051645(n)) = 30 * A051645(n) + 1. - Amiram Eldar, Feb 24 2025