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A308655 Alternating partial sums of the prime gaps. 1
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

(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 * A217663 A078701 A299766

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

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Last modified June 4 18:20 EDT 2020. Contains 334828 sequences. (Running on oeis4.)