A288815 Paired Jacobsthal function applied to the product of the first n primes.

2, 6, 18, 30, 66, 150, 192, 258, 366, 450, 570, 708, 894, 1044, 1284, 1422, 1656, 1902, 2190, 2460, 2622

Offset: 1

Author

Mario Ziller, Jun 17 2017

Keywords

• hard
• more
• nonn

Comments

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.

Links

• Mario Ziller, John F. Morack, Divisibility in paired progressions, Goldbach's conjecture, and the infinitude of prime pairs, arXiv:1706.00317 [math.NT], 2017.
• Mario Ziller, John F. Morack, On the computation of the generalised Jacobsthal function for paired progressions, arXiv:1706.03668 [math.NT], 2017.

Crossrefs

Cf. A072753, A048670.

Formula

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