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

0,2

Links

Table of n, a(n) for n=0..59.

Example

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.

Mathematica

Table[Length[ContinuedFraction[FromDigits[RealDigits[GoldenRatio, 10, n][[1]]]/10^(n-1)]], {n, 60}] (* Harvey P. Dale, May 28 2023 *)

Crossrefs

Cf. A065019.

Sequence in context: A060830 A080458 A147646 * A284510 A167523 A261811

Adjacent sequences: A080226 A080227 A080228 * A080230 A080231 A080232

Keyword

base,nonn

Author

Benoit Cloitre, Mar 17 2003

Status

approved