A130643 Numbers n such that 1 - Sum{k=1..n/2}A001223(2k-1)*(-1)^k = 0.

4, 8, 12, 22, 38, 302, 308, 464, 472, 476, 1186, 1884, 2006, 2026, 2106, 23636, 23656, 23698, 25984, 25990, 26706, 26924, 27000, 311914, 311938, 313866, 313880, 331676, 332002, 332676, 377102, 377634, 377670, 379026, 379090, 379108, 387618, 389076

Offset

1,1

Comments

Sequence has 177 terms < 10^8.

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.

Links

Table of n, a(n) for n=1..38.

Example

1 - ( -A001223(1) + A001223(3)) = 1-(-1+2) = 0, hence 4 is a term.
1 - ( -A001223(1) + A001223(3) - A001223(5) + A001223(7)) = 1-(-1+2-2+2) = 0, hence 8 is a term.

Mathematica

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}]

Crossrefs

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

Sequence in context: A128233 A092108 A015781 * A014617 A239053 A272708

Adjacent sequences: A130640 A130641 A130642 * A130644 A130645 A130646

Keyword

nonn

Author

Manuel Valdivia, Jun 20 2007

Status

approved