This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A245460 #14 Jul 24 2014 09:44:11 %S A245460 1,4,26,122,2102,23102,450452,9189182,193993802,3792578792, %T A245460 116454478142,5415133233512,252305096583542,11561510014033982, %U A245460 562558737261811292,31359378912013061912,1792403716245452460152,98060777857864844592572,4456958491657464897364262 %N A245460 Max (A245457(n), A245458(n)). %C A245460 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. %C A245460 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 %H A245460 Jens Kruse Andersen, <a href="/A245460/b245460.txt">Table of n, a(n) for n = 1..100</a> %H A245460 V. Shevelev, <a href="http://arXiv.org/abs/0912.4006">Theorems on twin primes-dual case</a>, arXiv:0912.4006 (Sections 10,11,14-18) %o A245460 (PARI) f(n,k) = ((prime(n)-k)!+2) % prod(i=1, n, prime(i)) %o A245460 a(n) = max(f(n,1), f(n,2)) \\ _Jens Kruse Andersen_, Jul 22 2014 %Y A245460 Cf. A245457, A245458, A244570, A244571, A244572. %K A245460 nonn %O A245460 1,2 %A A245460 _Vladimir Shevelev_, Jul 22 2014 %E A245460 More terms from _Jens Kruse Andersen_, Jul 22 2014