A308655 Alternating partial sums of the prime gaps.

1, -1, 1, -3, -1, -5, -3, -7, -1, -3, 3, -1, 1, -3, 3, -3, -1, -7, -3, -5, 1, -3, 3, -5, -1, -3, 1, -1, 3, -11, -7, -13, -11, -21, -19, -25, -19, -23, -17, -23, -21, -31, -29, -33, -31, -43, -31, -35, -33, -37, -31, -33, -23, -29, -23, -29, -27, -33, -29, -31

Offset

1,4

Comments

Does this sequence change sign infinitely often?

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{k=1..n} ((-1)^(k+1))*(prime(k+1) - prime(k)).

Mathematica

Table[Sum[((-1)^(k + 1)) (Prime[k + 1] - Prime[k]), {k, 1, n}], {n, 70}] (* Vincenzo Librandi, Jul 02 2019 *)

Prog

(PARI) a(n) = sum(k=1, n, ((-1)^(k+1))*(prime(k+1) - prime(k))); \\ Michel Marcus, Jun 14 2019
(Magma) [&+[((-1)^(k+1))*(NthPrime(k+1)-NthPrime(k)): k in [1..n]]: n in [1..100]]; // Vincenzo Librandi, Jul 02 2019

Crossrefs

Cf. A000040, A001223 (prime gaps), A274828.

Sequence in context: A099549 A334212 A082725 * A356365 A217663 A078701

Adjacent sequences: A308652 A308653 A308654 * A308656 A308657 A308658

Keyword

sign

Author

Marc Morgenegg, Jun 14 2019

Extensions

More terms from Michel Marcus, Jun 14 2019

Status

approved