A376759 Number of composite numbers c with n < c <= 2*n.

0, 1, 2, 2, 4, 4, 5, 6, 6, 6, 8, 8, 10, 11, 11, 11, 13, 14, 15, 16, 16, 16, 18, 18, 19, 20, 20, 21, 23, 23, 24, 25, 26, 26, 27, 27, 28, 29, 30, 30, 32, 32, 34, 35, 35, 36, 38, 39, 39, 40, 40, 40, 42, 42, 42, 43, 43, 44, 46, 47, 49, 50, 51, 51, 52, 52, 54, 55, 55, 55, 57, 58, 60, 61, 61, 61, 62, 63, 64, 65, 66, 66, 68, 68, 69, 70, 70, 71, 73, 73, 73, 74, 75, 76, 77, 77

Offset: 1

Author

N. J. A. Sloane, Oct 20 2024

Keywords

• nonn

Comments

This completes the set of four: A307912, A376759, A307989, and A075084. Since it is not clear which ones are the most important, and they are easily confused, all four are now in the OEIS.

Links

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

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

chi := proc(n) if n <= 3 then 0 else n - numtheory:-pi(n) - 1; fi; end; # A065855
A376759 := proc(n) chi(2*n) - chi(n); end;
a := [seq(A376759(n),n=1..120)];

Mathematica

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

Python

from sympy import primepi
def A376759(n): return n+primepi(n)-primepi(n<<1) # Chai Wah Wu, Oct 20 2024

Formula

a(n) = A000720(n) - A000720(2*n) + n. - Paolo Xausa, Oct 22 2024