A198195 a(n) is the smallest prime(m) such that the interval (prime(m)*n, prime(m+1)*n) contains exactly five primes.

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

Alois P. Heinz, Table of n, a(n) for n = 2..100

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

Cf. A195871, A187809, A187810, A187812.

Sequence in context: A236004 A024019 A159686 * A142819 A183058 A256709

Adjacent sequences: A198192 A198193 A198194 * A198196 A198197 A198198

Keyword

nonn

Author

Vladimir Shevelev and Peter J. C. Moses, Jan 07 2013

Status

approved