A288815 - OEIS

%I #13 Aug 03 2017 05:02:43

%S 2,6,18,30,66,150,192,258,366,450,570,708,894,1044,1284,1422,1656,

%T 1902,2190,2460,2622

%N Paired Jacobsthal function applied to the product of the first n primes.

%C There is a conjecture about an upper bound on this sequence. Let p_n be the n-th prime. If a(n) < p_n^2 - p_n holds for n>=3 then Goldbach's conjecture and the twin prime conjecture hold as well.

%H Mario Ziller, John F. Morack, <a href="https://arxiv.org/abs/1706.00317">Divisibility in paired progressions, Goldbach's conjecture, and the infinitude of prime pairs</a>, arXiv:1706.00317 [math.NT], 2017.

%H Mario Ziller, John F. Morack, <a href="https://arxiv.org/src/1706.03668v1/anc/full_details.pdf">On the computation of the generalised Jacobsthal function for paired progressions</a>, arXiv:1706.03668 [math.NT], 2017.

%F a(n) = 6*A072753(n) + 6, for n>=3.

%Y Cf. A072753, A048670.

%K hard,more,nonn

%O 1,1

%A _Mario Ziller_, Jun 17 2017