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

%I A257125 #50 Jul 01 2024 16:38:39
%S A257125 7,11,13,17,1277,88789,113143,113147,855709,74266249,182403491,
%T A257125 226449521,252277007,408936947,521481197,626927443,910935911,
%U A257125 964669609,1042090781,1116452627,1209950867,1422475909,1459270271,1645175087,2117861719,2335215973,2558211559,2843348351,2873599429,2966003057,3447123283,3947480417
%N A257125 Initial members of prime 9-tuplets (or nonuplets).
%C A257125 Primes prime(m) such that prime(m+8) = prime(m) + 30. - _Zak Seidov_, Jul 06 2015
%H A257125 Zak Seidov, <a href="/A257125/b257125.txt">Table of n, a(n) for n = 1..651</a> (Essentially original b-file by Tim Johannes Ohrtmann, just added a(1)=7 and corrected EndOfFile)
%H A257125 Tony Forbes and Norman Luhn, <a href="http://www.pzktupel.de/ktuplets.htm">Smallest Prime k-tuplets</a>
%t A257125 {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 *)
%t A257125 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 *)
%o A257125 (PARI) main(size)=v=vector(size); i=0; m=1; while(i<size, if(prime(m)+30===prime(m+8),v[i++]=prime(m));m++;); v \\ _Anders Hellström_, Jul 08 2015
%o A257125 (Magma) [NthPrime(n): n in [0..2*10^4] | NthPrime(n+8) eq (NthPrime(n) + 30)]; // _Vincenzo Librandi_, Jul 08 2015
%Y A257125 Initial members of all of the first prime k-tuplets:
%Y A257125 twin primes: A001359.
%Y A257125 prime triples: A007529 out of A022004, A022005.
%Y A257125 prime quadruplets: A007530.
%Y A257125 prime 5-tuples: A086140 out of A022007, A022006.
%Y A257125 prime sextuplets: A022008.
%Y A257125 prime septuplets: A257124 out of A022009, A022010.
%Y A257125 prime octuplets: A065706 out of A022011, A022012, A022013.
%Y A257125 prime nonuplets: this sequence out of A022547, A022548, A022545, A022546.
%Y A257125 prime decaplets: A257127 out of A027569, A027570.
%Y A257125 prime 11-tuplets: A257129 out of A213646, A213647.
%Y A257125 prime 12-tuplets: A257131 out of A213601, A213645.
%Y A257125 prime 13-tuplets: A257135 out of A214947, A257137, A257138, A257139, A257140, A257141.
%Y A257125 prime 14-tuplets: A257166 out of A257167, A257168.
%Y A257125 prime 15-tuplets: A257169 out of A257304, A257305, A257306, A257307.
%Y A257125 prime 16-tuplets: A257308 out of A257369, A257370.
%Y A257125 prime 17-tuplets: A257373 out of A257374, A257375, A257376, A257377.
%K A257125 nonn
%O A257125 1,1
%A A257125 _Tim Johannes Ohrtmann_, Apr 16 2015