A051645 Primes p such that 30*p+1 is also prime.

2, 5, 7, 11, 19, 23, 41, 43, 61, 67, 71, 79, 89, 109, 113, 131, 137, 167, 181, 193, 223, 229, 233, 277, 281, 313, 317, 331, 337, 359, 383, 439, 443, 457, 461, 467, 491, 503, 509, 541, 547, 593, 599, 607, 641, 691, 701, 733, 739, 743, 751, 769, 797, 821, 823

Offset: 1

Author

Labos Elemer

Keywords

• nonn
• easy

Comments

A002110(3)*p+1 and p are primes.

Examples

			p = 19 is in the sequence because 30*p+1 = 571 is also prime.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)

Crossrefs

Cf. A002110, A005384, A005385, A007693, A051646.

Programs

Magma

[p: p in PrimesUpTo(900) | IsPrime(30*p+1)]; // Vincenzo Librandi, Apr 11 2013

Mathematica

Select[Prime[Range[900]], PrimeQ[30 # + 1] &] (* Vincenzo Librandi, Apr 11 2013 *)

PARI

isok(k) = isprime(k) && isprime(30*k+1); \\ Amiram Eldar, Feb 24 2025

Formula

a(n) = (A051646(n)-1)/30. - Amiram Eldar, Feb 24 2025