

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
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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*(1x)) 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 Selfdifferential Functional Equations, Real Anal. Exchange 32 (2006), no. 1, 2954.
G. A. Edgar, Examples of self differential functions
J. Fabius, A probabilistic example of a nowhere analytic C^inftyfunction, Probability Theory and Related Fields, June 1966, Volume 5, Issue 2, pp. 173174.
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



