A118288 Decimal expansion of the Embree-Trefethen constant.

7, 0, 2, 5, 8

Offset

0,1

Comments

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

Named after the American mathematicians Mark Patrick Embree (b. 1974) and Lloyd Nicholas Trefethen (b. 1955). - Amiram Eldar, Jun 16 2021

References

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

Links

Table of n, a(n) for n=0..4.

M. Embree and L. N. Trefethen, Growth and decay of random Fibonacci sequences, Roy. Soc. London Proc. Ser. A, Math. Phys. Eng. Sci., Vol. 455 (1999), pp. 2471-2485.

Eric Weisstein's World of Mathematics, Random Fibonacci Sequence.

Wikipedia, Embree-Trefethen constant.

Example

0.70258...

Crossrefs

Cf. A078416.

Sequence in context: A261167 A197014 A244979 * A094153 A243374 A309608

Adjacent sequences: A118285 A118286 A118287 * A118289 A118290 A118291

Keyword

nonn,cons,hard,more,nice

Author

Eric W. Weisstein, Apr 22 2006

Status

approved