A104036 a(n) = number m such that the golden mean phi's m-th convergent F(m+1)/F(m) matches its actual value to n decimal places (here F(m) is the m-th Fibonacci number A000045(m)).

4, 7, 10, 12, 14, 17, 19, 21, 23, 26, 29, 31, 33, 36, 37, 40, 43, 46, 48, 50, 52, 55, 57, 59, 62, 64, 66, 69, 71, 74, 76, 79, 80, 84, 85, 89, 90, 92, 96, 98, 101, 102, 105, 107, 109, 112, 115, 117, 119, 122, 125, 127, 128, 132, 134, 136, 138, 141, 143, 145, 148

Offset

1,1

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..1000

David Consiglio, Jr., Python program

F. Richman, Continued fractions

Example

a(1) = 4 because F(5) / F(4) = 5/3 = 1.666... which is the lowest Fibonacci ratio that matches Phi (1.618...) to 1 decimal place.
a(2) = 7 because F(7) / F(6) = 21 / 13 = 1.615... which is the lowest Fibonacci ratio that matches Phi to 2 decimal places.

Crossrefs

Cf. A001622.

Sequence in context: A047845 A097703 A310674 * A214641 A178598 A310675

Adjacent sequences: A104033 A104034 A104035 * A104037 A104038 A104039

Keyword

nonn,base

Author

Lekraj Beedassy, Mar 31 2005

Extensions

a(7)-a(8) corrected and extended by David Consiglio, Jr., Oct 13 2015

Status

approved