

A104036


a(n) = number m such that the golden mean phi's mth convergent F(m+1)/F(m) matches its actual value to n decimal places (here F(m) is the mth 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
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OFFSET

1,1


LINKS



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



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



