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

2,1

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).

Links

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

Formula

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

Example

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.

Crossrefs

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

Sequence in context: A240584 A139988 A140005 * A124584 A074979 A375974

Adjacent sequences: A198316 A198317 A198318 * A198320 A198321 A198322

Keyword

nonn

Author

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

Status

approved