A187812 a(n) is the smallest prime(m) such that the interval (prime(m)*n, prime(m+1)*n) contains exactly four primes.

89, 23, 13, 23, 17, 5, 5, 5, 5, 11, 11, 71, 2, 2, 2, 2, 29, 2, 101, 59, 2, 107, 107, 239, 197, 71, 419, 107, 197, 347, 311, 179, 281, 827, 1277, 269, 827, 569, 1481, 1667, 1031, 1019, 617, 2081, 4337, 5651, 3767, 641, 3119, 2789, 2999, 11699, 4241, 8219, 4127

Offset

2,1

Comments

Conjecture. In the supposition that there are infinitely many twin primes, every term beginning with the sixth 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=6, and consider intervals of the form (6*prime(m), 6*prime(m+1)).
For 2, 3, 5, ..., the intervals (12,18), (18,30), (30,42), (42,66), (66,78), (78,102), (102,114)... contain 2, 3, 3, 5, 3, 5, 4,... primes. Hence the smallest such prime is 17.

Crossrefs

Cf. A195871, A187809, A187810.

Sequence in context: A036951 A051328 A166321 * A075483 A220135 A301827

Adjacent sequences: A187809 A187810 A187811 * A187813 A187814 A187815

Keyword

nonn

Author

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

Status

approved