A245460 Max (A245457(n), A245458(n)).

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

Offset: 1

Author

Vladimir Shevelev, Jul 22 2014

Keywords

• nonn

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)

Crossrefs

Cf. A245457, A245458, A244570, A244571, A244572.

Programs

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

Extensions

More terms from Jens Kruse Andersen, Jul 22 2014