A324859 Decimal expansion of 0.1990753..., an inflection point of a Hurwitz zeta fixed-point function.

1, 9, 9, 0, 7, 5, 3, 0, 3, 5, 4, 4, 7, 7, 2, 8, 5, 4, 9, 7, 1, 1, 3, 0, 0, 3, 5, 0, 7, 2, 2, 2, 8, 4, 2, 1, 6, 8, 8, 2, 8, 6, 6, 3, 2, 0, 1, 6, 3, 1, 5, 1, 0, 7, 6, 1, 0, 1, 4, 8, 1, 0, 1, 7, 7, 9, 7, 0, 6, 9, 3, 8, 2, 0, 3, 4, 0, 7, 2, 1, 0, 3, 6, 6, 9, 8, 1, 6, 4, 0, 4, 4, 7, 4, 9, 2, 4, 1, 9, 7

Offset

0,2

Comments

For real values of the parameter "a" between 0 and 1, a real fixed point "s" of the iterated Hurwitz zeta function [s = zetahurwitz(s, a)] lies on a curve that passes through A069857 (-0.295905...) and has a maximum tending toward 1. This curve has inflection points for a = 0.1990753... or 0.91964... . The fixed point "s" on this curve for the iteration "s = zetahurwitz(s, A324859)" is A324860 (0.5250984...).

Links

Table of n, a(n) for n=0..99.

Reikku Kulon, Plot of Hurwitz zeta fixed-point curve for 0 < a < 2 and -1 < s < +1.

Example

0.1990753035447728549711300350722284216882866320163...

Prog

(PARI) solve(t = 1/16, 1/2, derivnum(x = t, solve(v = -1, 1 - x, v - zetahurwitz(v, x)), 2); )

Crossrefs

Cf. A069857, A069995, A324860.

Sequence in context: A021838 A199960 A257176 * A090655 A334480 A229758

Adjacent sequences: A324856 A324857 A324858 * A324860 A324861 A324862

Keyword

nonn,cons

Author

Reikku Kulon, Mar 18 2019

Status

approved