A277255 Let A_n defined in the same way as A159559, but with initial term prime(n); a(n) is the smallest number m such that A_(n+1)(m) - A_n(m) > 6 or a(n)=0 if there is no such m.

0, 13, 0, 0, 9, 0, 0, 13, 0, 15, 0, 9, 0, 0, 11, 0, 17, 13, 11, 7, 5, 3, 2, 0, 11, 7, 5, 3, 2, 7, 5, 3, 2, 15, 0, 9, 0, 7, 5, 3, 2, 7, 5, 3, 2, 2, 9, 0, 7, 5, 3, 2, 0, 0, 11, 0, 7, 5, 3, 2, 2, 7, 5, 3, 2, 3, 2, 7, 5, 3, 2, 11, 7, 5, 3, 2, 3, 2, 2, 3, 2, 11, 7

Offset: 2

Author

Vladimir Shevelev and Peter J. C. Moses, Oct 22 2016

Keywords

• nonn

Comments

A277118 is a subsequence. In contrast to A277118, the sequence contains some terms greater than 17. The first occurrence for 19 is n = 7061; the first occurrence for 21 is n = 214612 and the first occurrence for 23 is n = 30572.

Links

• Peter J. C. Moses, Table of n, a(n) for n = 2..5001
• Vladimir Shevelev, Peter J. C. Moses, Constellations of primes generated by twin primes, arXiv:1610.03385 [math.NT], 2016.

Crossrefs

Cf. A159559, A277118.

Formula

a(n)=2 if and only if prime(n+1) - prime(n) >=8.