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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified January 16 13:35 EST 2022. Contains 350376 sequences. (Running on oeis4.)