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%I #3 Mar 30 2012 18:35:47
%S 2,4,6,8,12,14,190,194,306,308,462,464,472,474,476,478,490,1884,1890,
%T 1938,23636,23656,23850,25226,25834,25984,26642,26650,26924,26998,
%U 27000,311922,313880,313946,331676,331762,331782,332676,377078,377518,377666
%N Numbers n such that 1 - S(n) = 0, where S(n) = (S(n-1) + A000040(n))*(-1)^n; S(0)=0, n=>1.
%C The terms are equal to A130642 for n/2 odd (100 terms) and to A130643 for n/2 even (86 terms).
%e S(11)=(..((((0+2)*-1)+3)*1)+5)*-1)+7)*1)+11)*- 1)+13)*1)+...+29)*1)+31)*-1 = -36, 1 - S(12)=1 - (-36 + 37)*1 = 0, hence 12 is a term.
%e S(13)=(..((((0+2)*-1)+3)*1)+5)*-1)+7)*1)+11)*- 1)+13)*1)+...+37)*1)+41)*-1 = -42, 1 - S(14)=1 - (-42 + 43)*1 = 0, hence 14 is a term.
%t S=0;a=0; Do[S=(S+Prime[n])*(-1)^n; If[1-S==0,a++; Print[a," ",n]], {n, 1, 10^8, 1}]
%Y Cf. A130642, A130643, A008347, A066033, A000040.
%K nonn
%O 1,1
%A _Manuel Valdivia_, Sep 26 2007