A162938 A 2-based alternate sum over the numbers from 0 to the n-th nonprime.

2, 5, 8, 11, 14, 25, 17, 20, 23, 40, 26, 29, 32, 55, 35, 38, 65, 41, 70, 44, 47, 50, 85, 53, 90, 56, 59, 100, 62, 65, 68, 115, 71, 74, 125, 77, 130, 80, 83, 140, 86, 145, 89, 92, 95, 160, 98, 165, 101, 104, 175, 107, 110, 113, 190, 116, 195, 119, 122, 205, 125, 128, 215

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 18 2009

Keywords

• nonn

Comments

Define a 2-based sum S(n) = Sum_{i=0..n} (2 - (-1)^i*i) = 2*n - (-1)^n*A152832(n).

a(n) is this sum evaluated at A141468(n).

Examples

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

Crossrefs

Cf. A141468.

Programs

Maple

A152832 := proc(n) option remember; if n = 0 then -2; else n-procname(n-1) ; fi; end:
A141468 := proc(n) option remember ; local a; if n <=2 then n-1; else for a from procname(n-1)+1 do if not isprime(a) then RETURN(a); fi; od: fi; end:
A162938 := proc(n) local npr; npr := A141468(n) ; 2*npr-(-1)^npr*A152832(npr) ; end:
seq(A162938(n),n=1..100) ; # R. J. Mathar, Jul 21 2009

Formula

a(n) = Sum_{x=0..n-th nonprime} (2 - x*(-1)^x). - Juri-Stepan Gerasimov, Jul 28 2009

Extensions

Definition edited by R. J. Mathar, Jul 21 2009