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A324859 Decimal expansion of 0.1990753..., an inflection point of a Hurwitz zeta fixed-point function. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified July 5 21:00 EDT 2020. Contains 335473 sequences. (Running on oeis4.)