cp's OEIS Frontend

A022013 Initial members of prime octuplets (p, p+6, p+8, p+14, p+18, p+20, p+24, p+26).

%I A022013 #59 Jul 21 2025 16:21:16
%S A022013 88793,284723,855713,1146773,6560993,69156533,74266253,218033723,
%T A022013 261672773,302542763,964669613,1340301863,1400533223,1422475913,
%U A022013 1837160183,1962038783,2117861723,2249363093,2272018733,2558211563
%N A022013 Initial members of prime octuplets (p, p+6, p+8, p+14, p+18, p+20, p+24, p+26).
%C A022013 All terms are congruent to 173 (modulo 210). - _Matt C. Anderson_, May 26 2015
%H A022013 Dana Jacobsen, <a href="/A022013/b022013.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Matt C. Anderson)
%H A022013 T. Forbes and Norman Luhn, <a href="http://www.pzktupel.de/ktuplets">Prime k-tuplets</a>
%H A022013 Stephan Ramon Garcia, Jeffrey Lagarias, and Ethan Simpson Lee, <a href="https://arxiv.org/abs/2206.01391">The error term in the truncated Perron formula for the logarithm of an L-function</a>, arXiv:2206.01391 [math.NT], 2022.
%H A022013 Norman Luhn and Hugo Pfoertner, <a href="https://pzktupel.de/SMArchiv/08tup3.7z">10 million terms of A022013</a>, 7z compressed (47.9 MB) (2021).
%F A022013 a(n) = 210*A357890(n) + 173. - _Hugo Pfoertner_, Nov 18 2022
%t A022013 Select[Prime[Range[200000]], Union[PrimeQ[# + {6, 8, 14, 18, 20, 24, 26}]] == {True} &] (* _Vincenzo Librandi_, Sep 30 2015 *)
%t A022013 Select[Prime[Range[125*10^6]],AllTrue[#+{6,8,14,18,20,24,26},PrimeQ]&] (* _Harvey P. Dale_, Jul 21 2025 *)
%o A022013 (Perl) use ntheory ":all"; say for sieve_prime_cluster(1,1e10, 6,8,14,18,20,24,26); # _Dana Jacobsen_, Sep 30 2015
%o A022013 (Magma) [p: p in PrimesUpTo(2*10^8) | forall{p+r: r in [6,8,14,18,20,24,26] | IsPrime(p+r)}]; // _Vincenzo Librandi_, Sep 30 2015
%o A022013 (PARI) forprime(p=2, 1e30, if (isprime(p+6) && isprime(p+8) && isprime(p+14) && isprime(p+18) && isprime(p+20) && isprime(p+24) && isprime(p+26) , print1(p", "))) \\ _Altug Alkan_, Sep 30 2015
%Y A022013 A065706 is the union of A022011, A022012 and A022013.
%Y A022013 A346998(n) = a(10^n).
%Y A022013 Cf. A347852, A347853, A357890.
%K A022013 nonn
%O A022013 1,1
%A A022013 _Warut Roonguthai_