A376759 - OEIS

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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

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OFFSET

1,3

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

FORMULA

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

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 *)

PROG

(Python)

from sympy import primepi

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

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.

Sequence in context: A089413 A159267 A127311 * A302929 A129229 A219029

Adjacent sequences: A376756 A376757 A376758 * A376760 A376761 A376762

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 20 2024

STATUS

approved