A130643 - OEIS

%I #3 Mar 30 2012 18:35:47

%S 4,8,12,22,38,302,308,464,472,476,1186,1884,2006,2026,2106,23636,

%T 23656,23698,25984,25990,26706,26924,27000,311914,311938,313866,

%U 313880,331676,332002,332676,377102,377634,377670,379026,379090,379108,387618,389076

%N Numbers n such that 1 - Sum{k=1..n/2}A001223(2k-1)*(-1)^k = 0.

%C Sequence has 177 terms < 10^8.

%C Being prime(n) = 1 - Sum{k=1..n-1}A000040(k)*(-1)^Floor(k/2), for n/2 even and, prime(n) = (1 - Sum{k=1..n- 1}A000040(k)*(-1)^Floor(k/2))*(-1), for n/2 odd.

%e 1 - ( -A001223(1) + A001223(3)) = 1-(-1+2) = 0, hence 4 is a term.

%e 1 - ( -A001223(1) + A001223(3) - A001223(5) + A001223(7)) = 1-(-1+2-2+2) = 0, hence 8 is a term.

%t S=0; a=0; Do[S=S+(Prime[2*k]-Prime[2*k-1])*(-1)^k; If[1-S==0, a++; Print[a, " ", 2*k]], {k, 1, 10^8, 1}]

%Y Cf. A127596, A128039, A001223, A000101, A002386.

%K nonn

%O 1,1

%A _Manuel Valdivia_, Jun 20 2007