A257167 - OEIS

%I #24 Apr 11 2022 22:04:42

%S 11,21817283854511261,841262446570150721,1006587882969594041,

%T 2682372491413700201,5009128141636113611,7126352574372296381,

%U 7993822923596334941,12870536149631655611,15762479629138737611,22811391659969177381,25593071201116914611,25908823282383706781,42408988436795325461,44360646117391789301,54533311498517797061,54872625531142644341,55603189618237916771,60815831883653681951

%N Numbers n such that n, n+2, n+6, n+8, n+12, n+18, n+20, n+26, n+30, n+32, n+36, n+42, n+48 and n+50 are all prime.

%H Dana Jacobsen, <a href="/A257167/b257167.txt">Table of n, a(n) for n = 1..185</a> [first 57 terms computed by Betsis, Säfholm, Forbes, Hadley, Vlesycit, and Waldvogel (1982-2009)]

%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/14tup1.zip">Table of n, a(n) for n = 1..919</a>

%o (Perl) use ntheory ":all"; say for sieve_prime_cluster(1, 10**17, 2, 6, 8, 12, 18, 20, 26, 30, 32, 36, 42, 48, 50); # _Dana Jacobsen_, Oct 18 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, A257137, A257138, A257139, A257140, A257141.

%Y prime 14-tuplets: A257166 out of this sequence, 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 17 2015

%E a(32) corrected by _Dana Jacobsen_, Oct 18 2015