A103655 Indices of primes which are the average of two successive semiprimes.

3, 16, 19, 24, 30, 32, 40, 47, 54, 62, 63, 68, 75, 80, 87, 93, 94, 95, 115, 124, 126, 129, 133, 136, 138, 157, 160, 162, 167, 169, 175, 177, 179, 187, 196, 205, 222, 232, 233, 239, 240, 247, 258, 265, 267, 270, 274, 277, 279, 298, 299, 318, 327, 335, 336, 339

Offset: 1

Author

Zak Seidov, Feb 12 2005

Keywords

• nonn

Examples

			19 is a member because p(19)=67; 65 and 69 are two successive semiprimes closest to 67 and 67=(65+69)/2.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Corresponding primes: A103654. Primes: A000040, semiprimes: A001358, number of primes between two successive semiprimes: A088700, number of semiprimes between two successive primes: A103668.

Cf. A000040, A088700, A103654, A001358, A103668, A103669.

Programs

Mathematica

PrimePi[#]&/@Select[Mean/@Partition[Select[Range[2500],PrimeOmega[#]==2&],2,1],PrimeQ] (* Harvey P. Dale, Sep 08 2024 *)

Formula

a(n)=pi(A103654(n)).