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
Keywords
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).
Crossrefs
Programs
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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 -
Mathematica
Select[Prime[Range[200000]], Union[PrimeQ[# + {6, 8, 14, 18, 20, 24, 26}]] == {True} &] (* Vincenzo Librandi, Sep 30 2015 *) Select[Prime[Range[125*10^6]],AllTrue[#+{6,8,14,18,20,24,26},PrimeQ]&] (* Harvey P. Dale, Jul 21 2025 *) -
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
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Perl
use ntheory ":all"; say for sieve_prime_cluster(1,1e10, 6,8,14,18,20,24,26); # Dana Jacobsen, Sep 30 2015
Formula
a(n) = 210*A357890(n) + 173. - Hugo Pfoertner, Nov 18 2022
Comments