A130642 Numbers n such that 1 + Sum{k=1..n/2}A001223(2k-1)*(-1)^k = 0.

2, 6, 14, 190, 194, 200, 306, 462, 468, 474, 478, 490, 560, 1208, 1890, 1938, 23716, 23850, 25226, 25834, 25968, 26642, 26650, 26998, 48316, 311888, 311922, 313946, 331540, 331762, 331782, 377078, 377518, 377666, 377674, 377748, 378422, 378428

Offset

1,1

Comments

Sequence has 170 terms < 10^8.

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

Links

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

Example

1 + ( -A001223(1)) = 1+(-1) = 0, hence 2 is a term.
1 + ( -A001223(1) + A001223(3) - A001223(5)) = 1+(-1+2-2) = 0, hence 6 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: A333121 A131518 A222201 * A376406 A133933 A297574

Adjacent sequences: A130639 A130640 A130641 * A130643 A130644 A130645

Keyword

nonn

Author

Manuel Valdivia, Jun 20 2007

Status

approved