A128039 Numbers n such that 1 - Sum_{k=1..n-1} A001223(k)*(-1)^k = 0.

3, 6, 10, 13, 18, 26, 29, 218, 220, 223, 491, 535, 538, 622, 628, 3121, 3126, 3148, 3150, 3155, 3159, 4348, 4436, 4440, 4444, 4458, 4476, 4485, 4506, 4556, 4608, 4611, 4761, 5066, 5783, 5788, 12528, 1061290, 2785126, 2785691, 2867466, 2867469, 2872437

Offset

1,1

Comments

Sequence has 294 terms < 10^7. If n is in this sequence then prime(n) = abs(3 + 2*Sum_{k=1..n-1} prime(k)*(-1)^k).

Links

Table of n, a(n) for n=1..43.

Eric Weisstein's World of Mathematics, Prime Difference Function

Eric Weisstein's World of Mathematics, Prime Sums

Eric Weisstein's World of Mathematics, Alternating Series

Example

1 - ( -A001223(1) + A001223(2)) = 1-(-1+2) = 0, hence 3 is a term.
1 - ( -A001223(1) + A001223(2) - A001223(3) + A001223(4) - A001223(5)) = 1-(-1+2-2+4-2) = 0, hence 6 is a term.

Mathematica

S=0; a=0; Do[S=S+((Prime[k+1]-Prime[k])*(-1)^k); If[1-S==0, a++; Print[a, " ", k+1]], {k, 1, 10^7, 1}]

Crossrefs

Cf. A127596, A001223 (differences between consecutive primes), A000101 (increasing gaps between primes, upper end), A002386 (increasing gaps between primes, lower end), A066033.

Sequence in context: A267593 A248221 A189368 * A027428 A136850 A079248

Adjacent sequences: A128036 A128037 A128038 * A128040 A128041 A128042

Keyword

nonn

Author

Manuel Valdivia, May 07 2007

Status

approved