

A187812


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


4



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
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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



