A354879 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.

0, 1, 10, 22, 63, 131, 276, 567, 1170, 2164, 4021, 7441, 13500, 24362, 43865, 77904, 137326, 242183, 425850, 744892

Offset

1,3

Comments

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.

Links

Table of n, a(n) for n=1..20.

Formula

a(n) = last occurrence n in A114524 after recounting index of A114524 on index of the first Stieltjes gamma in set.

Example

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.

Mathematica

(* 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}]

Crossrefs

Cf. A114523, A114524, A354835, A354878.

Sequence in context: A043918 A033459 A255048 * A349847 A333104 A214959

Adjacent sequences: A354876 A354877 A354878 * A354880 A354881 A354882

Keyword

nonn,more

Author

Artur Jasinski, Jun 18 2022

Status

approved