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A130701 Decimal expansion of mu, a continued fraction first constructed from the Fibonacci numbers (A000045). 0
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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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

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, ....

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)....

REFERENCES

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

LINKS

Table of n, a(n) for n=1..105.

Joseph S. Madachy, A Fibonacci constant, Recreational Mathematics, Fibonacci Quarterly 6:6 (1968), p. 385.

MATHEMATICA

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

CROSSREFS

Cf. A000045, A113011.

Sequence in context: A293634 A125143 A200012 * A202021 A197507 A264992

Adjacent sequences:  A130698 A130699 A130700 * A130702 A130703 A130704

KEYWORD

cons,nonn

AUTHOR

Robert G. Wilson v, Jul 01 2007

STATUS

approved

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Last modified October 14 00:10 EDT 2019. Contains 327990 sequences. (Running on oeis4.)