A187809 a(n) is the smallest prime(m) such that the interval (prime(m)*n, prime(m+1)*n) contains exactly two primes.

5, 3, 17, 2, 2, 2, 41, 2, 2, 29, 2, 107, 137, 191, 179, 599, 239, 281, 857, 1427, 641, 809, 1061, 857, 1481, 1049, 1451, 1229, 1019, 1151, 3359, 3257, 2129, 2141, 1931, 1019, 4271, 4649, 2687, 4229, 16061, 4337, 16139, 6569, 9857, 4001, 4547, 17027, 40037

Offset

2,1

Comments

Conjecture. In the supposition that there are infinitely many twin primes, every term 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=4, and consider intervals of the form (4*prime(m), 4*prime(m+1)).
For 2, 3, 5, ..., the intervals (8,12), (12,20), (20,28), (28,44), (44,52), (52,68), (68,76)... contain 1, 3, 1, 5, 1, 4, 2,... primes. Hence the smallest such prime is 17.

Crossrefs

Cf. A195871.

Sequence in context: A292243 A105201 A184537 * A092893 A133172 A363686

Adjacent sequences: A187806 A187807 A187808 * A187810 A187811 A187812

Keyword

nonn

Author

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

Status

approved