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

Author

Manuel Valdivia, May 07 2007

Keywords

• nonn

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).

Examples

			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.
		

Links

• 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

Crossrefs

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

Programs

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}]