A052188 Primes p such that p, p+12, p+24 are consecutive primes.

199, 1499, 4397, 4679, 7829, 9859, 11287, 11399, 11719, 12829, 15149, 16607, 17419, 17839, 18329, 18719, 19727, 19937, 20149, 20509, 20719, 21649, 22039, 22247, 23789, 25609, 26029, 28057, 29587, 30047, 31039, 32467, 34159, 35117, 35839, 35899, 36217, 36809, 40099

Offset: 1

Author

Labos Elemer, Jan 28 2000

Keywords

• nonn

Comments

Corresponds to two consecutive 12's in A001223. - - M. F. Hasler, Jan 02 2020

Examples

			a(1) = 199, followed by the consecutive primes 199 + 12 = 211, 199 + 12 + 12 = 223.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Zak Seidov)
• OEIS wiki, Consecutive primes in arithmetic progression: CPAP with given gap, updated Jan. 2020.

Crossrefs

Subsequence of A031930.

Generalization of A047948 and A033451 if 6 replaced by 12.

Cf. A001223, A033447.

Programs

Magma

[p:p in PrimesUpTo(36000)| NextPrime(p)-p eq 12 and  NextPrime(p+12)-p eq 24]; // Marius A. Burtea, Jan 03 2020

Mathematica

Transpose[Select[Partition[Prime[Range[3800]],3,1], Union[Differences[#]] =={12}&]][[1]]  (* Harvey P. Dale, Apr 26 2011 *)

PARI

lista(nn) = {forprime(p=1, nn, q = nextprime(p+1); r = nextprime(q+1); if ((r-q==12) && (q-p==12), print1(p, ", ")););} \\ Michel Marcus, Jun 27 2015

Extensions

Name changed by Jon E. Schoenfield, May 30 2018