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

Author

Roger L. Bagula, Mar 18 2006

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A097454.

Programs

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 *)

PARI

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

Formula

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

Extensions

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