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A354878
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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.
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1
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0, 1, 3, 6, 17, 51, 98, 193, 387, 719, 1269, 2394, 4380, 7895, 14227, 25381, 44840, 79416, 140313, 245792, 428589, 746256
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OFFSET
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1,3
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COMMENTS
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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.
For the indices of the Stieltjes constants at which the last set of exactly n successive constants of the same sign begins, see A354879.
Sequence generated using the 10^6 Stieltjes constants computed by Krzysztof Maslanka.
a(23) > 10^6.
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LINKS
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Table of n, a(n) for n=1..22.
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FORMULA
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For n > 1, a(n) = A354835(k) + 1 such that A354835(k+1) - A354835(k) = n and k is smallest one available.
a(n) = first occurrence n in A114524 after recounting index of A114524 on index of the first Stieltjes gamma in set.
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EXAMPLE
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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.
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.
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MATHEMATICA
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(* 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}]
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CROSSREFS
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Cf. A114523, A114524, A354835, A354879.
Sequence in context: A307685 A360273 A287901 * A143093 A117712 A106158
Adjacent sequences: A354875 A354876 A354877 * A354879 A354880 A354881
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KEYWORD
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nonn,more
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AUTHOR
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Artur Jasinski, Jun 09 2022
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STATUS
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approved
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