A162939 A 1-based alternate sum over the numbers from 0 to prime(n).

1, 5, 8, 11, 17, 20, 26, 29, 35, 44, 47, 56, 62, 65, 71, 80, 89, 92, 101, 107, 110, 119, 125, 134, 146, 152, 155, 161, 164, 170, 191, 197, 206, 209, 224, 227, 236, 245, 251, 260, 269, 272, 287, 290, 296, 299, 317, 335, 341, 344, 350, 359, 362, 377, 386, 395, 404

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 18 2009

Keywords

• nonn

Comments

Define a 1-based sum S(n) = sum_{i=1..n} (1 - (-1)^i*i) = A014682(n).

a(n) is this sum evaluated for the upper limit prime(n) = A000040(n).

a(n) = prime(n) + (prime(n)+1)/2 for n>1. (E.g., 3 + 4/2 = 5, 5 + 6/2 = 8, 7 + 8/2 = 11, ....) - Vladimir Joseph Stephan Orlovsky, Nov 30 2009 [edited by Jon E. Schoenfield, Feb 10 2015]

Examples

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

Links

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

Crossrefs

Cf. A000040.

Programs

Maple

A014682 := proc(n) option remember; coeftayl( x*(2+x+x^2)/(1-x^2)^2,x=0,n) ; end:
A162939 := proc(n) A014682(ithprime(n)) ; end: seq(A162939(n),n=1..70) ; # R. J. Mathar, Jul 21 2009

Mathematica

f[n_]:=n/2; lst={};Do[p=Prime[n];AppendTo[lst,p+f[p+1]],{n,2,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 30 2009 *)

Extensions

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