The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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)). 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 9 13:19 EDT 2023. Contains 363180 sequences. (Running on oeis4.)