A114523 a(n) is the sign of the n-th Stieltjes constant.

1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1

Offset

0,1

Comments

In other words, a(n) is the sign of the coefficient of s^n in the expansion of zeta(1-s) where zeta is the Riemann zeta function. - Jianing Song, May 22 2026

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Krzysztof Maślanka, Asymptotic Properties of Stieltjes Constants, arXiv:2210.07244 [math.NT], 2022.

Eric Weisstein's World of Mathematics, Stieltjes Constants.

Wikipedia, Stieltjes constants.

Example

0.57722, -0.072816, -0.0096904, 0.0020538, 0.0023254, ..., so the first terms are 1,-1,-1,1,1,...

Mathematica

a[n_] := Sign[StieltjesGamma[n]]; Array[a, 100, 0] (* Amiram Eldar, May 22 2026 *)

Crossrefs

Cf. A114524, A394583 (indices of 1), A395455 (indices of -1).

Sequence in context: A212159 A106400 A112865 * A130151 A143431 A064179

Adjacent sequences: A114520 A114521 A114522 * A114524 A114525 A114526

Keyword

sign

Author

Eric W. Weisstein, Dec 06 2005

Status

approved