A239579 a(n) = |{0 < k <= n: prime(prime(prime(k*n))) - 2 is prime}|.

1, 0, 1, 0, 0, 2, 3, 2, 0, 3, 1, 2, 2, 3, 2, 2, 1, 3, 3, 1, 1, 1, 8, 4, 3, 1, 2, 4, 2, 2, 4, 5, 3, 4, 5, 3, 6, 4, 6, 3, 5, 5, 6, 3, 3, 10, 5, 10, 4, 3, 6, 4, 4, 7, 6, 5, 3, 3, 6, 5, 6, 3, 5, 9, 3, 6, 5, 8, 4, 9, 9, 10, 7, 12, 4, 9, 7, 7, 10, 11

Offset: 1

Author

Zhi-Wei Sun, Mar 21 2014

Keywords

• nonn

Comments

Conjecture: (i) a(n) > 0 for all n > 9.

(ii) If n > 0 is not equal to 5, then prime(prime(k*n)) + 2 is prime for some k = 1, ..., n.

Examples

			a(3) = 1 since prime(prime(prime(1*3))) - 2 = prime(prime(5)) - 2 = prime(11) - 2 = 31 - 2 = 29 is prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..3000
• Zhi-Wei Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014.

Crossrefs

Cf. A000040, A001359, A006512, A238573.

Programs

Mathematica

p[n_]:=PrimeQ[Prime[Prime[Prime[n]]]-2]
a[n_]:=Sum[If[p[k*n],1,0],{k,1,n}]
Table[a[n],{n,1,80}]