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

88793, 284723, 855713, 1146773, 6560993, 69156533, 74266253, 218033723, 261672773, 302542763, 964669613, 1340301863, 1400533223, 1422475913, 1837160183, 1962038783, 2117861723, 2249363093, 2272018733, 2558211563

Offset

1,1

Comments

All terms are congruent to 173 (modulo 210). - Matt C. Anderson, May 26 2015

Links

Dana Jacobsen, Table of n, a(n) for n = 1..10000 (first 1000 terms from Matt C. Anderson)

T. Forbes and Norman Luhn, Prime k-tuplets

Stephan Ramon Garcia, Jeffrey Lagarias, and Ethan Simpson Lee, The error term in the truncated Perron formula for the logarithm of an L-function, arXiv:2206.01391 [math.NT], 2022.

Norman Luhn and Hugo Pfoertner, 10 million terms of A022013, 7z compressed (47.9 MB) (2021).

Formula

a(n) = 210*A357890(n) + 173. - Hugo Pfoertner, Nov 18 2022

Mathematica

Select[Prime[Range[200000]], Union[PrimeQ[# + {6, 8, 14, 18, 20, 24, 26}]] == {True} &] (* Vincenzo Librandi, Sep 30 2015 *)

Prog

(Perl) use ntheory ":all"; say for sieve_prime_cluster(1, 1e10, 6, 8, 14, 18, 20, 24, 26); # Dana Jacobsen, Sep 30 2015
(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
(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

Crossrefs

A065706 is the union of A022011, A022012 and A022013.

A346998(n) = a(10^n).

Cf. A347852, A347853, A357890.

Sequence in context: A031857 A346998 A022548 * A347853 A233038 A205835

Adjacent sequences: A022010 A022011 A022012 * A022014 A022015 A022016

Keyword

nonn

Author

Warut Roonguthai

Status

approved