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A272343 Decimal expansion of F(1/3), where F(x) is the Fabius function. 5
1, 8, 0, 1, 6, 5, 1, 1, 4, 8, 0, 1, 4, 8, 1, 9, 0, 6, 9, 5, 5, 7, 3, 3, 4, 3, 5, 9, 3, 1, 0, 2, 4, 1, 2, 2, 8, 6, 7, 9, 0, 7, 8, 0, 0, 0, 8, 1, 7, 4, 1, 6, 3, 2, 5, 6, 4, 0, 4, 3, 8, 5, 7, 3, 3, 2, 0, 2, 9, 5, 5, 6, 4, 3, 5, 4, 1, 5, 8, 4, 7, 2, 5, 5, 4, 9, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The Fabius function F(x) is the smooth monotone increasing function on [0, 1] satisfying F(0) = 0, F(1) = 1, F'(x) = 2*F(2*x) for 0 < x < 1/2, F'(x) = 2*F(2*(1-x)) for 1/2 < x < 1. It is infinitely differentiable at every point in the interval, but is nowhere analytic.

The numeric value of F(1/3) was calculated using Wynn's epsilon method applied to a sequence of piecewise polynomial approximations to the Fabius function.

LINKS

Vladimir Reshetnikov, Table of n, a(n) for n = 0..189

Yuri Dimitrov, G. A. Edgar, Solutions of Self-differential Functional Equations, Real Anal. Exchange 32 (2006), no. 1, 29--54.

G. A. Edgar, Examples of self differential functions

J. Fabius, A probabilistic example of a nowhere analytic C^infty-function, Probability Theory and Related Fields, June 1966, Volume 5, Issue 2, pp. 173-174.

Wikipedia, Fabius function

EXAMPLE

0.1801651148014819069557334359310241228679078...

CROSSREFS

Sequence in context: A321107 A198117 A241215 * A011314 A021559 A167176

Adjacent sequences:  A272340 A272341 A272342 * A272344 A272345 A272346

KEYWORD

nonn,cons,hard

AUTHOR

Vladimir Reshetnikov, Apr 26 2016

STATUS

approved

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Last modified August 10 06:23 EDT 2020. Contains 336368 sequences. (Running on oeis4.)