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

1,1

Comments

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A044693 A185662 A140726 * A142320 A305172 A316760

Adjacent sequences: A051643 A051644 A051645 * A051647 A051648 A051649

Keyword

nonn,easy

Author

Labos Elemer

Status

approved