A178768 Decimal expansion of real constant in an explicit counterexample to the Lagarias-Wang finiteness conjecture.

7, 4, 9, 3, 2, 6, 5, 4, 6, 3, 3, 0, 3, 6, 7, 5, 5, 7, 9, 4, 3, 9, 6, 1, 9, 4, 8, 0, 9, 1, 3, 4, 4, 6, 7, 2, 0, 9, 1, 3, 2, 7, 3, 7, 0, 2, 3, 6, 0, 6, 4, 3, 1, 7, 3, 5, 8, 0, 2, 4, 0, 4, 5, 4, 5, 9, 3, 0, 7, 7, 5, 6, 4, 5, 6, 5, 6, 1, 1, 0, 3, 5, 0, 6, 7, 1, 2

Offset

0,1

Links

Table of n, a(n) for n=0..86.

Kevin G. Hare, Ian D. Morris, Nikita Sidorov, and Jacques Theys, An explicit counterexample to the Lagarias-Wang finiteness conjecture, arXiv:1006.2117 [math.OC], 2010-2011.

Kevin G. Hare, Ian D. Morris, Nikita Sidorov, and Jacques Theys, An explicit counterexample to the Lagarias-Wang finiteness conjecture, Advances in Mathematics 226 (2011), 4667-4701.

J. C. Lagarias and Y. Wang, The finiteness conjecture for the generalized spectral radius of a set of matrices, Linear Algebra Appl., 214 (1995), 17-42.

Formula

Equals Product_{n >= 1} (1 - t(n-1)/(t(n)*t(n+1)))^((-1)^n*Fibonacci(n+1)), where t(n) = A022405(n+1) and Fibonacci(n) = A000045(n). See Theorem 1.1 of Hare et al. (2010, 2011). - Michel Marcus, May 10 2019

Example

0.74932654633036755794396194809134467209132737023606431735802...

Prog

(PARI) t(n) = if (n==0, 1, if (n==1, 2, if (n==2, 2, t(n-1)*t(n-2) - t(n-3)))); \\ A022405
prodinf(n=1, (1 - t(n-1)/(t(n)*t(n+1)))^((-1)^n*fibonacci(n+1))) \\ Michel Marcus, Jun 14 2015; May 10 2019

Crossrefs

Cf. A000045, A022405.

Sequence in context: A271173 A242909 A259147 * A008568 A019795 A200305

Adjacent sequences: A178765 A178766 A178767 * A178769 A178770 A178771

Keyword

cons,nonn

Author

Jonathan Vos Post, Jun 11 2010

Extensions

More terms from Amiram Eldar, May 15 2021

Status

approved