A198319 a(n) is the smallest prime(m) such that the interval (prime(m)*n, prime(m+1)*n) contains exactly six primes.

113, 139, 23, 19, 37, 7, 19, 13, 67, 43, 3, 3, 3, 5, 11, 59, 5, 17, 59, 107, 17, 29, 71, 2, 2, 2, 239, 101, 191, 2, 2, 41, 227, 137, 179, 239, 419, 281, 149, 179, 227, 137, 1151, 239, 347, 809, 569, 1091, 1289, 1427, 191, 827, 1697, 1721, 1049, 1049, 3299

Offset: 2

Author

Vladimir Shevelev and Peter J. C. Moses, Jan 07 2013

Keywords

• nonn

Comments

Conjecture. In the supposition that there are infinitely many twin primes, every term beginning with the 12th is 2 or in A001359 (lesser of twin primes).

Examples

			Let n=19, and consider intervals of the form (19*prime(m), 19*prime(m+1)).  For 2, 3, 5, ..., the intervals (38,57), (57,95), (95,133), (133,209), (209,247), (247,323), (323,361)... contain 4, 8, 8, 14, 7, 13, 6,... primes. Hence the smallest such prime is 17.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..100

Crossrefs

Cf. A195871, A187809, A187810, A187812, A198195.

Formula

lim a(n) = infinity, as n goes to infinity.