A118288 - OEIS

%I #27 Sep 13 2023 08:27:55

%S 7,0,2,5,8

%N Decimal expansion of the Embree-Trefethen constant.

%C Suppose b(1) = 1 and b(n+1) = +-b(n) +- x*b(n-1) with the four choices of sign made with equal probability. Embree and Trefethen show that if x is less than this constant, b(n) tends to 0; otherwise, |b(n)| increases without bound. - _Charles R Greathouse IV_, Jul 19 2013

%C Named after the American mathematicians Mark Patrick Embree (b. 1974) and Lloyd Nicholas Trefethen (b. 1955). - _Amiram Eldar_, Jun 16 2021

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, section 1.2.4, p. 10.

%H M. Embree and L. N. Trefethen, <a href="http://people.maths.ox.ac.uk/trefethen/publication/PDF/1999_86.pdf">Growth and decay of random Fibonacci sequences</a>, Roy. Soc. London Proc. Ser. A, Math. Phys. Eng. Sci., Vol. 455 (1999), pp. 2471-2485.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RandomFibonacciSequence.html">Random Fibonacci Sequence</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Embree%E2%80%93Trefethen_constant">Embree-Trefethen constant</a>.

%e 0.70258...

%Y Cf. A078416.

%K nonn,cons,hard,more,nice

%O 0,1

%A _Eric W. Weisstein_, Apr 22 2006