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 A198319 a(n) is the smallest prime(m) such that the interval (prime(m)*n, prime(m+1)*n) contains exactly six primes. 2
 113, 139, 23, 19, 37, 7, 19, 13, 67, 43, 3, 3, 3, 5, 11, 59, 5, 17, 59, 107, 17, 29, 71, 2, 2, 2, 239, 101, 191, 2, 2, 41, 227, 137, 179, 239, 419, 281, 149, 179, 227, 137, 1151, 239, 347, 809, 569, 1091, 1289, 1427, 191, 827, 1697, 1721, 1049, 1049, 3299 (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 12th 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=19, and consider intervals of the form (19*prime(m), 19*prime(m+1)).  For 2, 3, 5, ..., the intervals (38,57), (57,95), (95,133), (133,209), (209,247), (247,323), (323,361)... contain 4, 8, 8, 14, 7, 13, 6,... primes. Hence the smallest such prime is 17. CROSSREFS Cf. A195871, A187809, A187810, A187812, A198195. Sequence in context: A240584 A139988 A140005 * A124584 A074979 A164920 Adjacent sequences:  A198316 A198317 A198318 * A198320 A198321 A198322 KEYWORD nonn AUTHOR Vladimir Shevelev and Peter J. C. Moses, Jan 07 2013 STATUS approved

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Last modified September 21 20:10 EDT 2021. Contains 347598 sequences. (Running on oeis4.)