A131196 Numbers n such that 1 + S(n) = 0, where S(n) = (S(n-1) + A000040(n))*(-1)^n; S(0)=0, n=>1.

22, 38, 200, 302, 468, 560, 1186, 1208, 2006, 2026, 2106, 23698, 23716, 25968, 25990, 26706, 48316, 311888, 311914, 311938, 313866, 331540, 332002, 377102, 377634, 377670, 377748, 378428, 378452, 378996, 379026, 379090, 387618, 388140, 389398

Offset: 1

Author

Manuel Valdivia, Sep 26 2007

Keywords

• nonn

Comments

The terms are equal to A130642 for n/2 even (70 terms) and to A130643 for n/2 odd (91 terms).

Examples

			S(21)=(..((((0+2)*-1)+3)*1)+5)*-1)+7)*1)+11)*- 1)+13)*1)+...+71)*1)+73)*-1 = -80, 1 + S(22) =1 + (-80 + 79)*1 = 0, hence 22 is a term.
S(37)=(..((((0+2)*-1)+3)*1)+5)*-1)+7)*1)+11)*- 1)+13)*1)+...+151)*1)+157)*-1 = -164, 1 + S(38) =1 + (-164 + 163)*1 = 0, hence 38 is a term.
		

Crossrefs

Cf. A130642, A130643, A008347, A066033, A000040.

Programs

Mathematica

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