A116568 Difference between n and the absolute value of the difference between number of nonprimes not exceeding n and number of primes not exceeding n.

0, 2, 2, 4, 4, 6, 6, 8, 8, 8, 10, 10, 12, 12, 12, 12, 14, 14, 16, 16, 16, 16, 18, 18, 18, 18, 18, 18, 20, 20, 22, 22, 22, 22, 22, 22, 24, 24, 24, 24, 26, 26, 28, 28, 28, 28, 30, 30, 30, 30, 30, 30, 32, 32, 32, 32, 32, 32, 34, 34, 36, 36, 36, 36, 36, 36, 38, 38, 38, 38, 40, 40, 42

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Formula

a(n) = n - Abs[A097454(n)].

Example

a(11)=10 because the nonprimes not exceeding 11 are 1,4,6,8,9 and 10, the primes not exceeding 11 are 2,3,5,7 and 11 and 11-abs(6-5)=10.

Maple

with(numtheory): seq(n-abs(n-2*pi(n)), n=1..73);

Mathematica

Table[n-Abs[2*PrimePi[n]-n], {n, 80}] (* Harvey P. Dale, Oct 08 2015 *)

Prog

(PARI) for(n=1, 50, print1(n - abs(2*primepi(n) - n) , ", ")) \\ G. C. Greubel, Sep 20 2017

Crossrefs

Cf. A097454.

Sequence in context: A179291 A004079 A096494 * A239933 A061106 A352928

Adjacent sequences: A116565 A116566 A116567 * A116569 A116570 A116571

Keyword

nonn

Author

Roger L. Bagula, Mar 18 2006

Extensions

Edited by N. J. A. Sloane, Apr 05 2006

Status

approved