A246514 Number of composite numbers between prime(n) and 2*prime(n) exclusive.

0, 1, 3, 4, 7, 9, 12, 14, 17, 22, 23, 27, 31, 33, 37, 41, 45, 48, 53, 56, 59, 63, 67, 72, 77, 80, 83, 87, 90, 94, 103, 107, 111, 113, 121, 124, 128, 134, 138, 144, 148, 150, 158, 160, 164, 166, 175, 184, 188, 190, 193, 199, 201, 209, 214, 219, 226, 228, 234

Offset: 1

Author

Odimar Fabeny, Aug 28 2014

Keywords

• nonn
• easy

Examples

			2 P 4 = 0,
3 4 P 6 = 1,
5 6 P 8 9 10 = 3,
7 8 9 10 P 12 P 14 = 4,
11 12 P 14 15 16 P 18 P 20 21 22 = 7
and so on.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Related sequences:

Primes (p) and composites (c): A000040, A002808, A000720, A065855.

Primes between p(n) and 2*p(n): A063124, A070046; between c(n) and 2*c(n): A376761; between n and 2*n: A035250, A060715, A077463, A108954.

Composites between p(n) and 2*p(n): A246514; between c(n) and 2*c(n): A376760; between n and 2*n: A075084, A307912, A307989, A376759.

Programs

Maple

A246515 := proc(n) local p;  p:=ithprime(n); n - 1 + p - numtheory:-pi(2*p - 1); end; # N. J. A. Sloane, Oct 20 2024
[seq(A246515(n),n=1..120)];

Mathematica

Table[Prime[n] - PrimePi[2*Prime[n]] + n - 1, {n, 100}] (* Paolo Xausa, Oct 22 2024 *)

PARI

s=[]; forprime(p=2, 1000, n=0; for(q=p+1, 2*p-1, if(!isprime(q), n++)); s=concat(s, n)); s \\ Colin Barker, Aug 28 2014

PARI

a(n)=prime(n)+n-1-primepi(2*prime(n))
vector(100, n, a(n)) \\ Faster program. Jens Kruse Andersen, Aug 28 2014

Python

from sympy import prime, primepi
def A246514(n): return (m:=prime(n))+n-1-primepi(m<<1) # Chai Wah Wu, Oct 22 2024

Formula

a(n) + A070046(n) = number of numbers between prime(n) and 2*prime(n), which is prime(n)-1. - N. J. A. Sloane, Aug 28 2014

Extensions

More terms from Colin Barker, Aug 28 2014