A125683 Numerator of Sum_{k=1..n} (-1)^(k+1) * 1/(k*(k+1)).

1, 1, 5, 11, 2, 79, 331, 479, 493, 5297, 2701, 69071, 70061, 69203, 55963, 471181, 158395, 8960447, 45108541, 44831407, 45083347, 1031626241, 518238043, 5160071143, 5180664331, 15484789693, 15537907043, 64166447971, 64357670431

Offset

1,3

Comments

Numbers n such that a(n) is prime are listed in A125684(n) = {3,4,5,6,7,8,10,13,14,18,21,22,26,27,28,32,33,35,51,54,58,67,76,89,100,...}.

Corresponding primes are listed in A125685(n) = a(A125684(n)) = {5,11,2,79,331,479,5297,70061,69203,8960447,45083347,...}.

Links

Robert Israel, Table of n, a(n) for n = 1..2307

Formula

a(n) = numerator of Sum_{k=1..n} (-1)^(k+1) * 1/(k*(k+1)).

Maple

map(numer, ListTools:-PartialSums([seq((-1)^(k+1)/k/(k+1), k=1..40)])); # Robert Israel, Apr 13 2021

Mathematica

Table[Numerator[Sum[(-1)^(k+1)*1/(k(k+1)), {k, 1, n}]], {n, 1, 40}]

Prog

(PARI) a(n) = numerator(sum(k=1, n, (-1)^(k+1) * 1/(k*(k+1)))); \\ Michel Marcus, Apr 13 2021

Crossrefs

Cf. A125684, A125685.

Sequence in context: A201457 A111118 A159199 * A125685 A098147 A100298

Adjacent sequences: A125680 A125681 A125682 * A125684 A125685 A125686

Keyword

nonn

Author

Alexander Adamchuk, Nov 30 2006

Status

approved