A180476 Smallest k>0 such that q=p+6k, 6kp+q, 6kp-q, 6kq+p and 6kq-p are simultaneously prime, or 0 if no such k exists, where p=A000040(n) is the n-th prime.

0, 0, 1, 10, 518, 1, 154, 120, 1, 2, 8, 15, 911, 226, 24, 9470, 189, 2766, 8224, 4998, 1730, 49, 106, 3114, 2030, 155, 231, 4, 119, 195, 2354, 31, 1749, 29, 7, 2806, 11704, 11, 1380, 561, 140, 553, 431, 50231, 65, 7, 1003, 1, 1905, 57, 456, 77, 231, 3346, 35, 301, 99, 106, 20, 1045, 71, 280, 1169, 231, 685, 440, 566, 385, 7994, 4095

Offset

1,4

Comments

It is conjectured that such a k>0 does exist for all primes > 3.

Links

M. F. Hasler, Table of n, a(n) for n = 1..6000

W. Sindelar, Certain Pairs of Consecutive Prime Numbers, in yahoo group "primenumbers".

W. Sindelar, David Broadhurst, Certain Pairs of Consecutive Prime Numbers, digest of 2 messages in primenumbers Yahoo group, Jan 20 - Jan 21, 2011.

Formula

a(n) = (A180481(n)-A000040(n))/6 for n>2.

Mathematica

sk[p_]:=Module[{k=1, q}, While[!AllTrue[{q=p+6k, 6k p+q, 6k p-q, 6k q+p, 6k q- p}, PrimeQ], k++]; k]; Join[{0, 0}, sk/@Prime[Range[3, 70]]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 12 2017 *)

Prog

(PARI) A180476(p, L=1e7)={ (3<p=prime(p)) & forstep( q=p+6, L, 6, isprime(q)|next; isprime(p*(q-p)+q)|next; isprime(p*(q-p)-q)|next; isprime(q*(q-p)+p)|next; isprime(q*(q-p)-p)|next; return((q-p)\6))

Crossrefs

A180481 gives the corresponding primes q.

Sequence in context: A356725 A163703 A218720 * A003399 A180359 A289200

Adjacent sequences: A180473 A180474 A180475 * A180477 A180478 A180479

Keyword

nonn

Author

M. F. Hasler, Jan 20 2011

Status

approved