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%I #16 Aug 20 2022 13:21:47
%S 0,1,10,22,63,131,276,567,1170,2164,4021,7441,13500,24362,43865,77904,
%T 137326,242183,425850,744892
%N a(n) is the index of the Stieltjes constant at the beginning of the last 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 first set of exactly n successive constants of the same sign begins, see A354878.
%C Sequence generated using the 10^6 Stieltjes constants computed by Krzysztof Maslanka.
%F a(n) = last 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 last (and the first also) Stieltjes constant that is not part of a run of more than one consecutive Stieltjes constant of the same sign.
%e a(5) = 63 because the set of 5 successive constants StieltjesGamma(63) = -390972.687, StieltjesGamma(64) = -1303180.71, StieltjesGamma(65) = -2845076.55, StieltjesGamma(66) = -4540526.609 and StieltjesGamma(67) = -4341905.139 have the same sign (negative), and no upper-indexed Stieltjes constant begins a set of exactly 5 consecutive Stieltjes constants of the same sign.
%t (* this sequence can be generated from A114524 *) f1=A114524;Table[b[n] = 0, {n, 1, 30}]; ile = 0; Do[b[f1[[n]]] = ile; ile = ile + f1[[n]], {n, 1, Length[f1]}]; tab = Table[b[n], {n, 1, 20}]
%Y Cf. A114523, A114524, A354835, A354878.
%K nonn,more
%O 1,3
%A _Artur Jasinski_, Jun 18 2022