cp's OEIS Frontend

A022011 Initial members of prime octuplets (p, p+2, p+6, p+8, p+12, p+18, p+20, p+26).

%I A022011 #56 Feb 24 2025 05:53:00
%S A022011 11,15760091,25658441,93625991,182403491,226449521,661972301,
%T A022011 910935911,1042090781,1071322781,1170221861,1394025161,1459270271,
%U A022011 1712750771,1742638811,1935587651,2048038451,2397437501,2799645461
%N A022011 Initial members of prime octuplets (p, p+2, p+6, p+8, p+12, p+18, p+20, p+26).
%C A022011 All terms are congruent to 11 (modulo 210). - _Matt C. Anderson_, May 26 2015
%D A022011 Martin Gardner, The Last Recreations, Chapter 12: Strong Laws of Small Primes, Springer-Verlag, 1997, pp. 191-205, especially p. 197.
%D A022011 Martin Gardner, Patterns in primes are a clue to the strong law of small numbers, Mathematical Games column, Scientific American, (December, 1980), pp. 20ff.
%H A022011 Dana Jacobsen, <a href="/A022011/b022011.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Matt C. Anderson)
%H A022011 T. Forbes and Norman Luhn, <a href="http://www.pzktupel.de/ktuplets.htm">Prime k-tuplets</a>
%H A022011 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 A022011 Norman Luhn and Hugo Pfoertner, <a href="https://pzktupel.de/SMArchiv/08tup1.7z">10 million terms of A022011</a>, 7z compressed (47.7 MB) (2021).
%t A022011 Select[Prime[Range[2 10^9]], Union[PrimeQ[# + {2, 6, 8, 12, 18, 20, 26}]] == {True} &] (* _Vincenzo Librandi_, Oct 01 2015 *)
%o A022011 (Perl) use ntheory ":all"; say for sieve_prime_cluster(1,1e10, 2,6,8,12,18,20,26); # _Dana Jacobsen_, Sep 30 2015
%o A022011 (Magma) [p: p in PrimesUpTo(4*10^8) | forall{p+r: r in [2,6,8,12,18,20,26] | IsPrime(p+r)}]; // _Vincenzo Librandi_, Oct 01 2015
%o A022011 (PARI) forprime(p=2, 10^30, if (isprime(p+2) && isprime(p+6) && isprime(p+8) && isprime(p+12) && isprime(p+18) && isprime(p+20) && isprime(p+26), print1(p", "))) \\ _Altug Alkan_, Oct 01 2015
%Y A022011 A065706 is the union of A022011, A022012 and A022013.
%Y A022011 A346996(n) = a(10^n).
%Y A022011 Cf. A347848, A347849.
%K A022011 nonn
%O A022011 1,1
%A A022011 _Warut Roonguthai_
%E A022011 Reference provided by _Harvey P. Dale_, May 10 2013
%E A022011 More terms from _Matt C. Anderson_, Dec 06 2013