A308655 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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