A130701 Decimal expansion of mu, a continued fraction first constructed from the Fibonacci numbers (A000045).

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

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 A342220 A197507

Adjacent sequences: A130698 A130699 A130700 * A130702 A130703 A130704

Keyword

cons,nonn

Author

Robert G. Wilson v, Jul 01 2007

Status

approved