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%I #30 Apr 11 2022 22:04:42
%S 1707898733581273,3266590043460823,4422879865247923,10907318641689703,
%T 32472302129057023,52590359764282573,60229684381540753,
%U 67893346321234513,93179596929433093,115458868925574253,140563537593599353,142977538681261363,148877505784397623,166362638531783773,232442516762530153,236585787518684683,255933372890105143,317294052871840123,325853825645632363,337188071215909993,344447962857168403
%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+36, n+46 and n+48 are all prime.
%H Vladimir Vlesycit and Matt C. Anderson and Dana Jacobsen, <a href="/A257138/b257138.txt">Table of n, a(n) for n = 1..802</a> [first 21 terms from Vladimir Vlesycit, first 90 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/13tup3.zip">Table of n, a(n) for n = 1..5290</a>
%o (PARI) Q=isprime;
%o isok(n) = Q(n) && Q(n+4) && Q(n+6) && Q(n+10) && Q(n+16) && Q(n+18) && Q(n+24) && Q(n+28) && Q(n+30) && Q(n+34) && Q(n+36) && Q(n+46) && Q(n+48); \\ _Michel Marcus_, Aug 04 2015
%o (Perl) use ntheory ":all"; say for sieve_prime_cluster(1, 10**16, 4,6,10,16,18,24,28,30,34,36,46,48); # _Dana Jacobsen_, Oct 09 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, this sequence, 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
%E a(18) corrected by _Matt C. Anderson_, Aug 03 2015
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