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A354879
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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.
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1
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0, 1, 10, 22, 63, 131, 276, 567, 1170, 2164, 4021, 7441, 13500, 24362, 43865, 77904, 137326, 242183, 425850, 744892
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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 first set of exactly n successive constants of the same sign begins, see A354878.
Sequence generated using the 10^6 Stieltjes constants computed by Krzysztof Maslanka.
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LINKS
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FORMULA
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a(n) = last 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 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.
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.
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MATHEMATICA
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(* 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}]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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