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%I #16 Feb 13 2013 23:58:29
%S 89,23,13,23,17,5,5,5,5,11,11,71,2,2,2,2,29,2,101,59,2,107,107,239,
%T 197,71,419,107,197,347,311,179,281,827,1277,269,827,569,1481,1667,
%U 1031,1019,617,2081,4337,5651,3767,641,3119,2789,2999,11699,4241,8219,4127
%N a(n) is the smallest prime(m) such that the interval (prime(m)*n, prime(m+1)*n) contains exactly four primes.
%C 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).
%H Alois P. Heinz, <a href="/A187812/b187812.txt">Table of n, a(n) for n = 2..100</a>
%F lim a(n) = infinity, as n goes to infinity.
%e Let n=6, and consider intervals of the form (6*prime(m), 6*prime(m+1)).
%e 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.
%Y Cf. A195871, A187809, A187810.
%K nonn
%O 2,1
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Jan 07 2013
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