A131694 Numbers k such that abs(S(k)) = A008347(k) is prime, where S(k) = S(k-1) + A000040(k)*(-1)^k; S(0) = 0.

1, 4, 6, 8, 10, 12, 18, 28, 32, 38, 42, 46, 50, 52, 54, 64, 68, 70, 72, 74, 76, 86, 88, 98, 100, 110, 126, 128, 130, 140, 146, 152, 162, 192, 202, 214, 226, 242, 252, 258, 264, 270, 290, 294, 304, 308, 314, 316, 320, 322, 332, 342, 348, 352, 358, 360

Offset

1,2

Comments

The sequence include as first term the only case where S(k) = -1 times a prime: S(1) = -2.

Links

Table of n, a(n) for n=1..56.

Example

S(3) = ((0+2*-1)+3*1)+5*-1 = -4, S(4) = -4 + 7*1 = 3 is prime, hence 4 is a term.
S(5) = ((((0+2*-1)+3*1)+5*-1)+7*1)+11*-1 = -8, S(6) = -8 + 13*1 = 5 is prime, hence 6 is a term.

Mathematica

S=0; Do[S=S+Prime[n]*(-1)^n; If[PrimeQ[S]==True, Print[n]], {n, 1, 10^3, 1}]

Crossrefs

Cf. A008347, A066033, A000040.

Sequence in context: A359330 A307542 A225510 * A053012 A359202 A096160

Adjacent sequences: A131691 A131692 A131693 * A131695 A131696 A131697

Keyword

nonn

Author

Manuel Valdivia, Oct 03 2007

Status

approved