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Search: id:A130701
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| A130701 |
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Decimal expansion of mu, a continued fraction first constructed from the Fibonacci numbers (A000045). |
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+0
1
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| 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; cons; graph; listen)
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OFFSET
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1,2
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COMMENT
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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)....
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REFERENCES
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Joseph S. Madachy, "Recreational Mathematics", Fibonacci Quarterly, 6, no. 6 (1968): 385-92.
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FORMULA
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Alfred S. Posamentier & Ingmar Lehmann, The (Fabulous) Fibonacci Numbers, Prometheus Books, NY, 2007, page ?.
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MATHEMATICA
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First@ RealDigits@ N[ Fold[ Last@#2 + First@#2/#1 &, 1, Partition[ Reverse@ Fibonacci@ Range@48, 2]], 111]
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CROSSREFS
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Cf. A000045, A113011.
Sequence in context: A101431 A120982 A125143 this_sequence A050000 A021721 A011428
Adjacent sequences: A130698 A130699 A130700 this_sequence A130702 A130703 A130704
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KEYWORD
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base,cons,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 01 2007
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