A049481 Primes p such that p + 30 is also prime.

7, 11, 13, 17, 23, 29, 31, 37, 41, 43, 53, 59, 67, 71, 73, 79, 83, 97, 101, 107, 109, 127, 137, 149, 151, 163, 167, 181, 193, 197, 199, 211, 227, 233, 239, 241, 251, 263, 277, 281, 283, 307, 317, 337, 349, 353, 359, 367, 379, 389, 401, 409, 419, 431, 433, 449

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

30 = A002110(3) is the 3rd primorial number.

p and p+30 are not necessarily consecutive primes. Initial segment of A045320 is identical, but 113 is not in this sequence because 113 + 30 = 143 is divisible by 13.

Examples

			7 is a term since it is prime and 7 + 30 = 37 is also prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..10000
• Hugo Pfoertner, Observed ratio n*log(a(n))/pi(a(n)) for n=10^7..5.6*10^9 with a conjectured extrapolation for large n (2024).

Crossrefs

Cf. A002110, A045320, A005597.

Cf. A001359, A023201, A049482, A049483, A049484, A049485, A154114.

Programs

Mathematica

lst={};Do[p=Prime[n];If[PrimeQ[p+30],AppendTo[lst,p]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 04 2009 *)
Select[Prime[Range[100]],PrimeQ[#+30]&] (* Harvey P. Dale, Apr 28 2012 *)

PARI

isok(p) = isprime(p) && isprime(p + 30); \\ Amiram Eldar, Mar 15 2025

Formula

Assuming Polignac's conjecture and the first Hardy-Littlewood conjecture: Limit_{n->oo} n*log(a(n))/primepi(a(n)) = (16/3)*A005597 = 3.52086... . - Alain Rocchelli, Oct 29 2024