

A237497


a(n) = {0 < k <= n/2: pi(k*(nk)) is prime}, where pi(.) is given by A000720.


8



0, 0, 0, 2, 2, 1, 2, 1, 1, 0, 1, 4, 3, 1, 1, 1, 3, 2, 6, 2, 2, 2, 4, 1, 1, 3, 3, 3, 1, 3, 3, 7, 4, 5, 4, 6, 5, 5, 3, 3, 3, 5, 7, 4, 1, 6, 7, 7, 5, 4, 1, 2, 3, 5, 5, 6, 8, 8, 6, 4, 9, 8, 6, 3, 7, 9, 6, 5, 4, 10, 5, 4, 6, 6, 4, 9, 10, 6, 8, 7
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OFFSET

1,4


COMMENTS

Conjecture: a(n) > 0 for all n > 10, and a(n) = 1 for no n > 51. Moreover, for any integer n > 10, there is a positive integer k < n with 2*k + 1 and pi(k*(nk)) both prime.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..3000
Z.W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014


EXAMPLE

a(6) = 1 since 6 = 1 + 5 with pi(1*5) = 3 prime.
a(8) = 1 since 8 = 2 + 6 with pi(2*6) = pi(12) = 5 prime.
a(25) = 1 since 25 = 4 + 21 with pi(4*21) = pi(84) = 23 prime.
a(51) = 1 since 51 = 14 + 37 with pi(14*37) = pi(518) = 97 prime.


MATHEMATICA

p[k_, m_]:=PrimeQ[PrimePi[k*m]]
a[n_]:=Sum[If[p[k, nk], 1, 0], {k, 1, n/2}]
Table[a[n], {n, 1, 80}]


CROSSREFS

Cf. A000040, A000720, A237284, A237291, A237453, A237496.
Sequence in context: A221649 A090406 A152723 * A281191 A324496 A137454
Adjacent sequences: A237494 A237495 A237496 * A237498 A237499 A237500


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Feb 08 2014


STATUS

approved



