A376762 Number of composite numbers c in the range prime(n) < c <= 2*prime(n+1).

2, 5, 6, 11, 11, 16, 16, 21, 28, 25, 33, 35, 35, 41, 47, 51, 50, 59, 60, 61, 69, 71, 78, 85, 84, 85, 91, 92, 98, 117, 111, 117, 115, 131, 126, 134, 140, 142, 150, 154, 152, 168, 162, 168, 168, 187, 196, 192, 192, 197, 205, 203, 219, 220, 225, 232, 230, 240, 242, 242, 258, 271, 264, 265, 271, 290, 288, 300, 295, 301, 309, 317, 320, 325, 327, 334, 344, 344, 355, 364, 358

Offset: 1

Author

N. J. A. Sloane, Oct 29 2024

Keywords

• nonn

Examples

			a(2) = 5 because there are 5 composite numbers c in the range 3 < c <= 10, namely 4, 6, 8, 9, and 10.
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000720, A020900, A065855, A210497, A376759.

Programs

Mathematica

A376762[n_] := n - Prime[n] + 2*Prime[n+1] - PrimePi[2*Prime[n+1]];
Array[A376762, 100] (* Paolo Xausa, Oct 29 2024 *)

Python

from sympy import prime, nextprime, primepi
def A376762(n): return int(n-(p:=prime(n))+(q:=nextprime(p)<<1)-primepi(q)) # Chai Wah Wu, Oct 29 2024

Formula

a(n) = 2*q - pi(2*q) - p + n, where p = prime(n), q = prime(n+1), and pi() = A000720().

a(n) = A210497(n) - A020900(n+1) + n. - Paolo Xausa, Oct 29 2024