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%I #16 Feb 13 2013 23:58:29
%S 31,7,3,3,3,3,2,17,17,2,17,2,107,59,71,107,101,179,197,431,179,521,
%T 431,431,809,179,599,641,809,2081,1061,827,1949,809,2801,2381,1481,
%U 1697,2087,1697,4127,2801,3929,4019,3329,4517,17597,5477,6761,13829,12239,5639
%N a(n) is the smallest prime(m) such that the interval (prime(m)*n, prime(m+1)*n) contains exactly three primes.
%C 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).
%H Alois P. Heinz, <a href="/A187810/b187810.txt">Table of n, a(n) for n = 2..100</a>
%F lim a(n) = infinity, as n goes to infinity.
%e Let n=9, and consider intervals of the form (9*prime(m), 9*prime(m+1)).
%e 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.
%Y Cf. A195871, A187809.
%K nonn
%O 2,1
%A _Vladimir Shevelev_ and _Peter J. C. Moses_, Jan 07 2013