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Numbers k such that the k-th and (k+1)st Stieltjes constants have opposite signs.
3

%I #23 Jun 09 2022 02:28:32

%S 0,2,5,9,12,16,21,25,30,35,40,45,50,56,62,67,73,79,85,91,97,104,110,

%T 117,123,130,136,143,150,157,164,171,178,185,192,200,207,214,222,229,

%U 237,244,252,259,267,275,282,290,298,306,314,322,330,338,346,354,362,370,378,386,395

%N Numbers k such that the k-th and (k+1)st Stieltjes constants have opposite signs.

%C Stieltjes constants change sign between StieltjesGamma(k) and StieltjesGamma(k+1).

%F a(n) = -1 + Sum_{i=0..n-1} A114524(i).

%e 0 is a term because StieltjesGamma(0) = 0.577216 (positive) and StieltjesGamma(1) = -0.0728158 (negative).

%e 5 is a term because StieltjesGamma(5) = 0.000793 (positive) and StieltjesGamma(6) = -0.0002387 (negative).

%t aa = {}; Do[If[Sign[StieltjesGamma[n]] != Sign[StieltjesGamma[n + 1]], AppendTo[aa, n]], {n, 0, 755}]; aa

%Y Cf. A114523, A114524.

%K nonn

%O 1,2

%A _Artur Jasinski_, Jun 07 2022