A163301 a(n) = Sum_{x=n-th even nonprime..n-th odd nonprime} -x*(-1)^x.

1, 3, 5, 7, 8, 8, 10, 10, 11, 13, 14, 14, 15, 15, 17, 17, 18, 20, 20, 21, 22, 22, 23, 23, 23, 24, 26, 28, 29, 29, 29, 29, 29, 29, 30, 31, 31, 33, 33, 33, 33, 35, 35, 36, 36, 37, 38, 38, 39, 39, 41, 41, 41, 41, 43, 45, 45, 45, 45, 45, 46, 46, 46, 46, 46, 47, 49, 50, 50, 52, 52

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 26 2009

Keywords

• nonn

Comments

Here n-th even nonprime = A163300(n), n-th odd nonprime = A014076(n) and A163300 U A014076 = A141468.

Seems to be essentially the same as A008508. - R. J. Mathar, May 30 2025

Examples

			a(1) = -0*(-1)^0 - 1*(-1)^1 = 0 + 1 = 1;
a(2) = -4*(-1)^4 - 5*(-1)^5 - 6*(-1)6 - 7*(-1)^7 - 8*(-1)^8 - 9*(-1)^9 = -4 + 5 - 6 + 7 - 8 + 9 = 3.
		

Crossrefs

Cf. A014076, A141468, A163300.

Programs

Maple

A163300 := proc(n) if n <= 2 then op(n,[0,4]) ; else for a from procname(n-1)+2 by 2 do if not isprime(a) then return a; end if; end do; end if; end proc:
A014076 := proc(n) if n = 1 then 1; else for a from procname(n-1)+2 by 2 do if not isprime(a) then return a ; end if; end do: end if; end proc:
A001057 := proc(n) (1-(-1)^n*(2*n+1))/4; end proc:
A163301 := proc(n) A001057( A014076(n)) - A001057(A163300(n)-1) ; end proc: seq(A163301(n),n=1..120) ; # R. J. Mathar, May 21 2010

Formula

a(n) = Sum_{x=A163300(n)..A014076(n)}-x*(-1)^x.

a(n) = A001057( A014076(n)) - A001057(A163300(n)-1). - R. J. Mathar, May 21 2010

Extensions

Corrected from a(39) onwards by R. J. Mathar, May 21 2010