A080229 Number of terms in the continued fraction for x, where x is the Golden ratio (phi=(1+sqrt(5))/2) truncated to n decimal digits.
1, 4, 8, 12, 12, 20, 18, 25, 29, 31, 34, 36, 39, 38, 44, 53, 51, 59, 60, 64, 64, 77, 71, 84, 81, 81, 89, 88, 92, 90, 93, 96, 110, 110, 114, 113, 122, 124, 123, 123, 140, 140, 139, 145, 155, 150, 165, 165, 159, 169, 170, 161, 173, 172, 194, 182, 187, 192, 190, 196
Offset: 0
Examples
Golden ratio truncated to 3 decimal places gives 1.618. The continued fraction for 1.618 is [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5] which contains 12 terms, hence a(3)=12.
Crossrefs
Cf. A065019.
Programs
-
Mathematica
Table[Length[ContinuedFraction[FromDigits[RealDigits[GoldenRatio,10,n][[1]]]/10^(n-1)]],{n,60}] (* Harvey P. Dale, May 28 2023 *)