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

11, 15760091, 25658441, 93625991, 182403491, 226449521, 661972301, 910935911, 1042090781, 1071322781, 1170221861, 1394025161, 1459270271, 1712750771, 1742638811, 1935587651, 2048038451, 2397437501, 2799645461

Offset

1,1

Comments

All terms are congruent to 11 (modulo 210). - Matt C. Anderson, May 26 2015

References

Martin Gardner, The Last Recreations, Chapter 12: Strong Laws of Small Primes, Springer-Verlag, 1997, pp. 191-205, especially p. 197.

Martin Gardner, Patterns in primes are a clue to the strong law of small numbers, Mathematical Games column, Scientific American, (December, 1980), pp. 20ff.

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 A022011, 7z compressed (47.7 MB) (2021).

Mathematica

Select[Prime[Range[2 10^9]], Union[PrimeQ[# + {2, 6, 8, 12, 18, 20, 26}]] == {True} &] (* Vincenzo Librandi, Oct 01 2015 *)

Prog

(Perl) use ntheory ":all"; say for sieve_prime_cluster(1, 1e10, 2, 6, 8, 12, 18, 20, 26); # Dana Jacobsen, Sep 30 2015
(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
(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

Crossrefs

A065706 is the union of A022011, A022012 and A022013.

A346996(n) = a(10^n).

Cf. A347848, A347849.

Sequence in context: A174089 A351239 A162861 * A175889 A347849 A295173

Adjacent sequences: A022008 A022009 A022010 * A022012 A022013 A022014

Keyword

nonn

Author

Warut Roonguthai

Extensions

Reference provided by Harvey P. Dale, May 10 2013

More terms from Matt C. Anderson, Dec 06 2013

Status

approved