OFFSET
1,1
COMMENTS
Conjecture: The terms of any feasible prime gap triple {a,b,c} to form a quadruple of consecutive primes are sums of terms of three consecutive subsequences of the infinite integer sequence with period (4,2,4,2,4,6,2,6). By this token all possible sequences of quadruples of consecutive primes can be generated, including those already in the OEIS.
LINKS
Robert Israel, Table of n, a(n) for n = 1..4147
EXAMPLE
The terms of the prime gap triple {10,18,2} are the sums of the terms of the following (arbitrarily chosen) subsequences ..., {4,2,4}, {6,2,6,4}, {2}, ... For n=3, a(n) = 17929 is the smallest prime of the third prime quadruple {17929, 17939, 17957, 17959}.
MAPLE
N:= 10^6; # to get all terms <= 6*N
Primes1:= select(isprime, {seq(6*i+1, i=1..N+5)}):
Primes5:= select(isprime, {seq(6*i+5, i=1..N+5)}):
Q:= `intersect`(Primes1, map(t->t-10, Primes5), map(t->t-28, Primes5), map(t->t-30, Primes1):
A215719:= select(t -> select(isprime, {seq(t+2*i, i=1..13)}) = {t+10}, Q): # Robert Israel, May 04 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
V.J. Pohjola, Aug 22 2012
EXTENSIONS
Definition and comment corrected by Robert Israel, May 04 2014
STATUS
approved