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A187809
a(n) is the smallest prime(m) such that the interval (prime(m)*n, prime(m+1)*n) contains exactly two primes.
6
5, 3, 17, 2, 2, 2, 41, 2, 2, 29, 2, 107, 137, 191, 179, 599, 239, 281, 857, 1427, 641, 809, 1061, 857, 1481, 1049, 1451, 1229, 1019, 1151, 3359, 3257, 2129, 2141, 1931, 1019, 4271, 4649, 2687, 4229, 16061, 4337, 16139, 6569, 9857, 4001, 4547, 17027, 40037
OFFSET
2,1
COMMENTS
Conjecture. In the supposition that there are infinitely many twin primes, every term is 2 or in A001359 (lesser of twin primes).
LINKS
FORMULA
lim a(n) = infinity, as n goes to infinity.
EXAMPLE
Let n=4, and consider intervals of the form (4*prime(m), 4*prime(m+1)).
For 2, 3, 5, ..., the intervals (8,12), (12,20), (20,28), (28,44), (44,52), (52,68), (68,76)... contain 1, 3, 1, 5, 1, 4, 2,... primes. Hence the smallest such prime is 17.
CROSSREFS
Cf. A195871.
Sequence in context: A292243 A105201 A184537 * A092893 A133172 A363686
KEYWORD
nonn
AUTHOR
STATUS
approved