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A198319
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a(n) is the smallest prime(m) such that the interval (prime(m)*n, prime(m+1)*n) contains exactly six primes.
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2
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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
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OFFSET
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2,1
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COMMENTS
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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).
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LINKS
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FORMULA
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lim a(n) = infinity, as n goes to infinity.
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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