A354878 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.

0, 1, 3, 6, 17, 51, 98, 193, 387, 719, 1269, 2394, 4380, 7895, 14227, 25381, 44840, 79416, 140313, 245792, 428589, 746256

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 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.

Links

Table of n, a(n) for n=1..22.

Formula

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.

Example

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.

Mathematica

(* 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}]

Crossrefs

Cf. A114523, A114524, A354835, A354879.

Sequence in context: A307685 A360273 A287901 * A143093 A117712 A106158

Adjacent sequences: A354875 A354876 A354877 * A354879 A354880 A354881

Keyword

nonn,more

Author

Artur Jasinski, Jun 09 2022

Status

approved