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A178768 Decimal expansion of real constant in an explicit counterexample to the Lagarias-Wang finiteness conjecture. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..58.

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

STATUS

approved

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Last modified September 18 20:22 EDT 2019. Contains 327181 sequences. (Running on oeis4.)