A162939 - OEIS

%I #12 Sep 17 2017 21:43:24

%S 1,5,8,11,17,20,26,29,35,44,47,56,62,65,71,80,89,92,101,107,110,119,

%T 125,134,146,152,155,161,164,170,191,197,206,209,224,227,236,245,251,

%U 260,269,272,287,290,296,299,317,335,341,344,350,359,362,377,386,395,404

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

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

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

%C 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]

%H G. C. Greubel, <a href="/A162939/b162939.txt">Table of n, a(n) for n = 1..5000</a>

%e a(1) = 1-1*(-1)^1+1-2*(-1)^2 = 1+1+1-2 = 1.

%e 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.

%p A014682 := proc(n) option remember; coeftayl( x*(2+x+x^2)/(1-x^2)^2,x=0,n) ; end:

%p A162939 := proc(n) A014682(ithprime(n)) ; end: seq(A162939(n),n=1..70) ; # _R. J. Mathar_, Jul 21 2009

%t 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 *)

%Y Cf. A000040.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Jul 18 2009

%E Definition edited by _R. J. Mathar_, Jul 21 2009