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A198195
a(n) is the smallest prime(m) such that the interval (prime(m)*n, prime(m+1)*n) contains exactly five primes.
3
509, 31, 7, 7, 7, 19, 13, 3, 3, 3, 97, 11, 17, 41, 41, 11, 2, 313, 2, 2, 137, 2, 2, 281, 227, 149, 149, 197, 281, 191, 101, 569, 191, 857, 827, 311, 569, 599, 431, 599, 1451, 1091, 809, 1019, 419, 1667, 2237, 4517, 5009, 3671, 1997, 1289, 1451, 3329, 3329
OFFSET
2,1
COMMENTS
Conjecture. In the supposition that there are infinitely many twin primes, every term beginning with the 20th is 2 or in A001359 (lesser of twin primes). The sequence is unbounded.
LINKS
EXAMPLE
Let n=14, and consider intervals of the form (14*prime(m), 14*prime(m+1)).
For 2, 3, 5, ..., the intervals (28,42), (42,70), (70,98), (98,154), (154,182), (182,238), (238,266)... contain 4, 6, 6, 11, 6, 9, 5,... primes. Hence the smallest such prime is 17.
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved