A364807 Numbers k such that abs(k - Sum_{m=2..k} pi(prime(k)/m)) is a prime number, where pi(k) is number of primes <= k.

2, 3, 5, 6, 8, 9, 18, 19, 21, 26, 29, 34, 48, 50, 56, 63, 69, 79, 84, 87, 95, 97, 99, 101, 110, 111, 132, 134, 139, 149, 151, 157, 160, 163, 164, 168, 171, 187, 201, 204, 209, 220, 222, 226, 227, 231, 244, 250, 256, 258, 268, 276, 282, 290, 292, 294, 296, 306

Offset: 0

Author

Saish S. Kambali, Aug 08 2023

Keywords

• nonn
• easy

Comments

Inspired by Ramanujan primes A104272.

Primes in common with A104272 are 2, 29, 97, 101, 149, 151, 227, ...; of those, the first twin prime pair is (149, 151).

pi(a(n)) ~ a(n)/log_2(n), where pi(a(n)) is number of primes <= a(n).

Examples

			k=6 is a term: abs(6 - Sum_{m=2..6} pi(prime(k)/m)) = abs(6 - 3 - 2 - 2 - 1 - 1) = abs(-3) = 3, which is prime.
		

Crossrefs

Cf. A000720, A104272.

Programs

Mathematica

Select[Range[320], PrimeQ[Abs[# - Sum[PrimePi[Prime[#]/m], {m, 2, #}]]] &] (* Amiram Eldar, Aug 08 2023 *)