A257137 - OEIS

%I #51 Apr 11 2022 22:04:42

%S 13,4289907938811613,5693002600430263,21817283854511263,

%T 48290946353555023,51165618791484133,53094081535451893,

%U 70219878257874463,98633358468021313,99142644093930373,104814760374339133,166784569423739203,167841416726358493,184601252515266523,263331429949004353,272039012072134243,339094624362619243,363319822006646623,363760043662280383,437335541550793003,455289126169953193

%N Numbers n such that n, n+4, n+6, n+10, n+16, n+18, n+24, n+28, n+30, n+34, n+40, n+46 and n+48 are all prime.

%C From _Robert Israel_, Aug 27 2015: (Start)

%C All terms after the first == 1483 (mod 2730).

%C n+4, n+16, n+28, n+46 are in A001359. (End)

%H Vladimir Vlesycit and Matt C. Anderson and Dana Jacobsen, <a href="/A257137/b257137.txt">Table of n, a(n) for n = 1..944</a> [first 21 terms from Vladimir Vlesycit, first 99 terms from Matt C. Anderson]

%H Tony Forbes and Norman Luhn, <a href="http://www.pzktupel.de/ktuplets.htm">Smallest Prime k-tuplets</a>

%H Norman Luhn, <a href="http://www.pzktupel.de/SMArchiv/13tup2.zip">Table of n, a(n) for n = 1..6305</a>

%o (PARI) is(n)=isp=isprime; isp(n) && isp(n+4) && isp(n+6) && isp(n+10) && isp(n+16) && isp(n+18) && isp(n+24) && isp(n+28) && isp(n+30) && isp(n+34) && isp(n+40) && isp(n+46) && isp(n+48) \\ _Anders Hellström_, Sep 05 2015

%o (Perl) use ntheory ":all"; say for sieve_prime_cluster(1,10**16, 4,6,10,16,18,24,28,30,34,40,46,48); # _Dana Jacobsen_, Oct 07 2015

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

%Y twin primes: A001359.

%Y prime triples: A007529 out of A022004, A022005.

%Y prime quadruplets: A007530.

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

%Y prime sextuplets: A022008.

%Y prime septuplets: A257124 out of A022009, A022010.

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

%Y prime nonuplets: A257125 out of A022547, A022548, A022545, A022546.

%Y prime decaplets: A257127 out of A027569, A027570.

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

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

%Y prime 13-tuplets: A257135 out of A214947, this sequence, A257138, A257139, A257140, A257141.

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

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

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

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

%K nonn

%O 1,1

%A _Tim Johannes Ohrtmann_, Apr 16 2015