A187810 a(n) is the smallest prime(m) such that the interval (prime(m)*n, prime(m+1)*n) contains exactly three primes.

31, 7, 3, 3, 3, 3, 2, 17, 17, 2, 17, 2, 107, 59, 71, 107, 101, 179, 197, 431, 179, 521, 431, 431, 809, 179, 599, 641, 809, 2081, 1061, 827, 1949, 809, 2801, 2381, 1481, 1697, 2087, 1697, 4127, 2801, 3929, 4019, 3329, 4517, 17597, 5477, 6761, 13829, 12239, 5639

Offset

2,1

Comments

Conjecture. In the supposition that there are infinitely many twin primes, every term beginning the fourth 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=9, and consider intervals of the form (9*prime(m), 9*prime(m+1)).
For 2, 3, 5, ..., the intervals (18,27), (27,45), (45,63), (63,99), (99,117), (117,153), (153,171)... contain 2, 5, 4, 7, 5, 6, 3,... primes. Hence the smallest such prime is 17.

Crossrefs

Cf. A195871, A187809.

Sequence in context: A040938 A040939 A040937 * A347592 A174129 A305663

Adjacent sequences: A187807 A187808 A187809 * A187811 A187812 A187813

Keyword

nonn

Author

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

Status

approved