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.
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
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jan 20 2011
STATUS
approved