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Decimal expansion of mu, a continued fraction first constructed from the Fibonacci numbers (A000045).
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%I #11 Aug 31 2012 17:22:36

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

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

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

%N Decimal expansion of mu, a continued fraction first constructed from the Fibonacci numbers (A000045).

%C 1+ 1/(2 +3/(5 + 8/(13 + ... .

%C Cited inaccurately in the second reference because they used only the first 28 terms.

%C Mu's simple continued fraction: 1, 2, 1, 1, 6, 3, 1, 1, 3, 2, 2, 2, 9, 1, 1, 1, 13, 1, 1, 189, 1, 10, 2, 6, 1, 6, 1, 5, 1, 59, 4, 24, 1, 42, 2, 1, 59, 1, 1, 2, 1, ....

%C Mu's increasingly larger PQ's: 1, 2, 6, 9, 13, 189, 1138, 4150, 6165, 90642, 90676, 526142, 757765, 20411415, 35535156, 271384175, ..., at positions: 1, 2, 5, 13, 17, 20, 454, 529, 708, 1832, 9248, 9631, 211052, 552035, 4552470, 4928425, (9290954)....

%D Alfred S. Posamentier & Ingmar Lehmann, The (Fabulous) Fibonacci Numbers, Prometheus Books, NY, 2007, page 171.

%H Joseph S. Madachy, <a href="http://www.fq.math.ca/Scanned/6-6/madachy.pdf">A Fibonacci constant</a>, Recreational Mathematics, Fibonacci Quarterly 6:6 (1968), p. 385.

%t First@ RealDigits@ N[ Fold[ Last@#2 + First@#2/#1 &, 1, Partition[ Reverse@ Fibonacci@ Range@48, 2]], 111]

%Y Cf. A000045, A113011.

%K cons,nonn

%O 1,2

%A _Robert G. Wilson v_, Jul 01 2007