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

1,1

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.

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).

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A002110, A045320, A005597.

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

Sequence in context: A103486 A086843 A260714 * A175412 A173700 A067557

Adjacent sequences: A049478 A049479 A049480 * A049482 A049483 A049484

Keyword

nonn

Author

Labos Elemer

Status

approved