A257125 Initial members of prime 9-tuplets (or nonuplets).

7, 11, 13, 17, 1277, 88789, 113143, 113147, 855709, 74266249, 182403491, 226449521, 252277007, 408936947, 521481197, 626927443, 910935911, 964669609, 1042090781, 1116452627, 1209950867, 1422475909, 1459270271, 1645175087, 2117861719, 2335215973, 2558211559, 2843348351, 2873599429, 2966003057, 3447123283, 3947480417

Offset: 1

Author

Tim Johannes Ohrtmann, Apr 16 2015

Keywords

• nonn

Comments

Primes prime(m) such that prime(m+8) = prime(m) + 30. - Zak Seidov, Jul 06 2015

Links

• Zak Seidov, Table of n, a(n) for n = 1..651 (Essentially original b-file by Tim Johannes Ohrtmann, just added a(1)=7 and corrected EndOfFile)
• Tony Forbes and Norman Luhn, Smallest Prime k-tuplets

Crossrefs

Initial members of all of the first prime k-tuplets:

twin primes: A001359.

prime triples: A007529 out of A022004, A022005.

prime quadruplets: A007530.

prime 5-tuples: A086140 out of A022007, A022006.

prime sextuplets: A022008.

prime septuplets: A257124 out of A022009, A022010.

prime octuplets: A065706 out of A022011, A022012, A022013.

prime nonuplets: this sequence out of A022547, A022548, A022545, A022546.

prime decaplets: A257127 out of A027569, A027570.

prime 11-tuplets: A257129 out of A213646, A213647.

prime 12-tuplets: A257131 out of A213601, A213645.

prime 13-tuplets: A257135 out of A214947, A257137, A257138, A257139, A257140, A257141.

prime 14-tuplets: A257166 out of A257167, A257168.

prime 15-tuplets: A257169 out of A257304, A257305, A257306, A257307.

prime 16-tuplets: A257308 out of A257369, A257370.

prime 17-tuplets: A257373 out of A257374, A257375, A257376, A257377.

Programs

Magma

[NthPrime(n): n in [0..2*10^4] | NthPrime(n+8) eq (NthPrime(n) + 30)]; // Vincenzo Librandi, Jul 08 2015

Mathematica

{p, q, r, s, t, u, v, w, x} = Prime@ Range@ 9; lst = {}; While[p < 1000000001, If[p + 30 == x, AppendTo[lst, p]; Print@ p]; {p, q, r, s, t, u, v, w, x} = {q, r, s, t, u, v, w, x, NextPrime@ x}]; lst (* Robert G. Wilson v, Jul 06 2015 *)
Select[Partition[Prime[Range[5 10^6]],9,1],#[[1]]+30==#[[9]]&][[;;,1]] (* The program generates the first 10 terms of the sequence. To generate more, increase the Range constant. *) (* Harvey P. Dale, Jul 01 2024 *)

PARI

main(size)=v=vector(size); i=0; m=1; while(iAnders Hellström, Jul 08 2015