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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
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved