



1, 4, 26, 122, 2102, 23102, 450452, 9189182, 193993802, 3792578792, 116454478142, 5415133233512, 252305096583542, 11561510014033982, 562558737261811292, 31359378912013061912, 1792403716245452460152, 98060777857864844592572, 4456958491657464897364262
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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



PROG

(PARI) f(n, k) = ((prime(n)k)!+2) % prod(i=1, n, prime(i))


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



