OFFSET
1,2
COMMENTS
Knowing a(n) <= (prime(n))^4 would yield an infinity of twin primes (in fact it is sufficient if this inequality holds for an arbitrary infinite subsequence k = k_n). See the Shevelev link, Section 17, Corollary 6.
Of course, (p_n)^4/A002110(n) is very small, but remember that sequence k_n could have arbitrary fast growth, for example, as (A002110(n)/(p_n)^4)^n. - Vladimir Shevelev, Jul 24 2014
LINKS
Jens Kruse Andersen, Table of n, a(n) for n = 1..100
V. Shevelev, Theorems on twin primes-dual case, arXiv:0912.4006 (Sections 10,11,14-18)
PROG
(PARI) f(n, k) = ((prime(n)-k)!+2) % prod(i=1, n, prime(i))
a(n) = max(f(n, 1), f(n, 2)) \\ Jens Kruse Andersen, Jul 22 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Jul 22 2014
EXTENSIONS
More terms from Jens Kruse Andersen, Jul 22 2014
STATUS
approved