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%I #27 Aug 20 2022 13:21:11
%S 0,1,3,6,17,51,98,193,387,719,1269,2394,4380,7895,14227,25381,44840,
%T 79416,140313,245792,428589,746256
%N a(n) is the index of the Stieltjes constant at the beginning of the first set of exactly n successive constants of the same sign.
%C Sets of n successive Stieltjes constants of the same sign occur only finitely many times, so for each n there exists a first and a last such set.
%C For the indices of the Stieltjes constants at which the last set of exactly n successive constants of the same sign begins, see A354879.
%C Sequence generated using the 10^6 Stieltjes constants computed by Krzysztof Maslanka.
%C a(23) > 10^6.
%F For n > 1, a(n) = A354835(k) + 1 such that A354835(k+1) - A354835(k) = n and k is smallest one available.
%F a(n) = first occurrence n in A114524 after recounting index of A114524 on index of the first Stieltjes gamma in set.
%e a(1) = 0 because StieltjesGamma(0) is the first (and the last also) Stieltjes constant that is not part of a run of more than one consecutive Stieltjes constant of the same sign.
%e a(5) = 17 because the set of 5 successive constants StieltjesGamma(17) = 0.000026277, StieltjesGamma(18) = 0.000307368, StieltjesGamma(19) = 0.000503605, StieltjesGamma(20) = 0.000466344 and StieltjesGamma(21) = 0.000104438 have the same sign (positive), and no lower-indexed Stieltjes constant begins a set of 5 consecutive Stieltjes constants of the same sign.
%t (* we can generate this sequence from A114524 *) fff=A114524;Table[a[n] = False, {n, 1, 30}]; Table[ b[n] = 0, {n, 1, 30}]; ile = 0; Do[ If[a[fff[[n]]] == False, a[fff[[n]]] = True; b[fff[[n]]] = ile]; ile = ile + fff[[n]], {n, 1, Length[fff]}]; tab = Table[b[n], {n, 1, 22}]
%Y Cf. A114523, A114524, A354835, A354879.
%K nonn,more
%O 1,3
%A _Artur Jasinski_, Jun 09 2022
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