OFFSET
1,1
COMMENTS
Goldston, Graham, Pintz, & Yilidirm give a conditional proof that this sequence is infinite; see their Theorem 4. - Charles R Greathouse IV, Jul 31 2013
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
D. A. Goldston, S. W. Graham, J. Pintz, C. Y. Yilidirm, Small gaps between primes or almost primes (2005)
K. Soundararajan, Small gaps between prime numbers: the work of Goldston-Pintz-Yildirim, Bull. Amer. Math. Soc. 44 (2007), pp. 1-18.
FORMULA
a(n) >> n log^2 n. - Charles R Greathouse IV, Jan 31 2017
PROG
(PARI) v=List([2]); p=3; forprime(q=5, 1e3, if(q-p<=6, listput(v, p)); p=q); Vec(v) \\ Charles R Greathouse IV, Jul 31 2013
(PARI) list(lim)=my(v=List(), p=2); forprime(q=3, nextprime(lim\1+1), if(q-p<7, listput(v, p)); p=q); Vec(v) \\ Charles R Greathouse IV, Jan 31 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 19 2006
STATUS
approved