A097454 a(n) = (number of nonprimes <= n) - (number of primes <= n).

1, 0, -1, 0, -1, 0, -1, 0, 1, 2, 1, 2, 1, 2, 3, 4, 3, 4, 3, 4, 5, 6, 5, 6, 7, 8, 9, 10, 9, 10, 9, 10, 11, 12, 13, 14, 13, 14, 15, 16, 15, 16, 15, 16, 17, 18, 17, 18, 19, 20, 21, 22, 21, 22, 23, 24, 25, 26, 25, 26, 25, 26, 27, 28, 29, 30, 29, 30, 31, 32, 31, 32, 31, 32, 33, 34, 35, 36, 35, 36, 37, 38, 37, 38, 39, 40, 41, 42, 41, 42, 43, 44, 45

Offset: 1

Author

Cino Hilliard, Aug 23 2004

Keywords

• sign
• easy

Examples

			a(7) = -1 because there are 3 nonprimes <= 7 (1,4 and 6) and 4 primes <= 7 (2,3,5 and 7).
		

Crossrefs

Cf. A000720, A010051, A062298, A072731.

Programs

Maple

with(numtheory): seq(n-2*pi(n), n=1..93); # Emeric Deutsch, Apr 01 2006

Mathematica

qp=0;lst={};Do[If[PrimeQ[n],AppendTo[lst,qp-=1],AppendTo[lst,qp+=1]],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, Mar 15 2010 *)
Accumulate[ -1 + 2 * Boole /@ Not /@ PrimeQ @ Range @ 100] (* Federico Provvedi, Oct 06 2013 *)

PARI

compsmprimes(n) = { for(x=1,n, y=composites(x) - pi(x); print1(y",") ) }
\\ The number of composite numbers less than or equal to n
composites(n) = { my(c,x); c=0; for(x=1,n, if(!isprime(x),c++); ); return(c) }
\\ pi(x) prime count function
pi(n) = { my(c,x); c=0;forprime(x=1,n,c++);return(c) }

Formula

a(n) = 1 + A072731(n).

a(n) = n - 2*pi(n) = n - 2*A000720(n). - Wesley Ivan Hurt, Jun 16 2013

a(n) - a(n-1) = 1 - 2*A010051(n) for n > 1. - Wesley Ivan Hurt, Dec 18 2018

a(n) = A062298(n) - A000720(n). - Michel Marcus, Jan 31 2019