A354879 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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