

A237712


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


3



0, 1, 1, 1, 0, 1, 3, 1, 3, 1, 2, 3, 4, 3, 3, 2, 2, 4, 4, 1, 5, 2, 2, 4, 2, 6, 8, 5, 6, 3, 4, 5, 2, 4, 3, 3, 8, 5, 8, 6, 4, 3, 10, 6, 6, 5, 1, 7, 4, 4, 6, 9, 6, 9, 5, 4, 6, 10, 3, 7, 7, 6, 3, 8, 13, 5, 8, 3, 9, 11, 4, 8, 6, 8, 11, 11, 11, 12, 13, 12, 10, 6, 7, 7, 4, 16, 10, 8, 9, 4, 6, 14, 11, 7, 4, 13, 10, 13, 8, 10
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OFFSET

1,7


COMMENTS

Conjecture: a(n) > 0 for all n > 5.
This implies that there are infinitely many positive integers m with m + pi(m) prime.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..2500
Z.W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014


EXAMPLE

a(6) = 1 since 2*6 + pi(2*6) = 12 + 5 = 17 is prime.
a(47) = 1 since 21*47 + pi(21*47) = 987 + 166 = 1153 is prime.


MATHEMATICA

p[n_]:=PrimeQ[n+PrimePi[n]]
a[n_]:=Sum[If[p[k*n], 1, 0], {k, 1, n1}]
Table[a[n], {n, 1, 100}]


CROSSREFS

Cf. A000040, A000720, A237578.
Sequence in context: A003636 A078929 A030728 * A227920 A138291 A201681
Adjacent sequences: A237709 A237710 A237711 * A237713 A237714 A237715


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Feb 24 2014


STATUS

approved



