A178768 - OEIS

%I #44 May 15 2021 03:55:25

%S 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,

%T 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,

%U 7,7,5,6,4,5,6,5,6,1,1,0,3,5,0,6,7,1,2

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

%H Kevin G. Hare, Ian D. Morris, Nikita Sidorov, and Jacques Theys, <a href="http://arxiv.org/abs/1006.2117">An explicit counterexample to the Lagarias-Wang finiteness conjecture</a>, arXiv:1006.2117 [math.OC], 2010-2011.

%H Kevin G. Hare, Ian D. Morris, Nikita Sidorov, and Jacques Theys, <a href="https://doi.org/10.1016/j.aim.2010.12.012">An explicit counterexample to the Lagarias-Wang finiteness conjecture</a>, Advances in Mathematics 226 (2011), 4667-4701.

%H J. C. Lagarias and Y. Wang, <a href="https://doi.org/10.1016/0024-3795(93)00052-2">The finiteness conjecture for the generalized spectral radius of a set of matrices</a>, Linear Algebra Appl., 214 (1995), 17-42.

%F 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

%e 0.74932654633036755794396194809134467209132737023606431735802...

%o (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

%o 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

%Y Cf. A000045, A022405.

%K cons,nonn

%O 0,1

%A _Jonathan Vos Post_, Jun 11 2010

%E More terms from _Amiram Eldar_, May 15 2021