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A187810
a(n) is the smallest prime(m) such that the interval (prime(m)*n, prime(m+1)*n) contains exactly three primes.
5
31, 7, 3, 3, 3, 3, 2, 17, 17, 2, 17, 2, 107, 59, 71, 107, 101, 179, 197, 431, 179, 521, 431, 431, 809, 179, 599, 641, 809, 2081, 1061, 827, 1949, 809, 2801, 2381, 1481, 1697, 2087, 1697, 4127, 2801, 3929, 4019, 3329, 4517, 17597, 5477, 6761, 13829, 12239, 5639
OFFSET
2,1
COMMENTS
Conjecture. In the supposition that there are infinitely many twin primes, every term beginning the fourth is 2 or in A001359 (lesser of twin primes).
LINKS
FORMULA
lim a(n) = infinity, as n goes to infinity.
EXAMPLE
Let n=9, and consider intervals of the form (9*prime(m), 9*prime(m+1)).
For 2, 3, 5, ..., the intervals (18,27), (27,45), (45,63), (63,99), (99,117), (117,153), (153,171)... contain 2, 5, 4, 7, 5, 6, 3,... primes. Hence the smallest such prime is 17.
CROSSREFS
Sequence in context: A040938 A040939 A040937 * A347592 A174129 A305663
KEYWORD
nonn
AUTHOR
STATUS
approved