A394583 Numbers k such that the k-th Stieltjes constant is positive.

0, 3, 4, 5, 10, 11, 12, 17, 18, 19, 20, 21, 26, 27, 28, 29, 30, 36, 37, 38, 39, 40, 46, 47, 48, 49, 50, 57, 58, 59, 60, 61, 62, 68, 69, 70, 71, 72, 73, 80, 81, 82, 83, 84, 85, 92, 93, 94, 95, 96, 97, 105, 106, 107, 108, 109, 110, 118, 119, 120, 121, 122, 123, 131, 132, 133, 134, 135, 136

Offset

1,2

Comments

In other words, numbers k such that the coefficient of s^k in the expansion of zeta(1-s) is positive, where zeta is the Riemann zeta function.

Union of {0} and [A354835(2*m)+1, A354835(2*m+1)] for all m >= 1.

Links

Jianing Song, Table of n, a(n) for n = 1..10013 (all terms up to A354835(1580) = 20009)

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

Eric Weisstein's World of Mathematics, Stieltjes Constants.

Wikipedia, Stieltjes constants.

Mathematica

Select[Range[0, 150], StieltjesGamma[#] > 0 &] (* Paolo Xausa, May 22 2026 *)

Crossrefs

Cf. A114523 (signs of Stieltjes constants), A354835. A395455 is the complement.

Sequence in context: A014463 A340015 A161983 * A047364 A274519 A139445

Adjacent sequences: A394580 A394581 A394582 * A394584 A394585 A394586

Keyword

nonn

Author

Jianing Song, May 22 2026

Status

approved