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

Author

Robert G. Wilson v, Jul 01 2007

Keywords

• cons
• nonn

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

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

Crossrefs

Cf. A000045, A113011.

Programs

Mathematica

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