A065019 -id:A065019 - cp's OEIS frontend

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

Benoit Cloitre, Mar 17 2003

			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.

Cf. A065019.

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

A080235 Number of terms in the continued fraction for (Pi truncated to n decimal digits).

Original entry on oeis.org

1, 2, 3, 6, 6, 8, 7, 11, 12, 13, 14, 21, 21, 23, 29, 28, 26, 31, 37, 36, 36, 42, 45, 48, 51, 47, 50, 53, 53, 62, 57, 55, 55, 68, 69, 52, 63, 66, 71, 79, 63, 66, 78, 90, 83, 82, 78, 85, 80, 91, 91, 90, 92, 93, 93, 107, 110, 103, 119, 120, 113, 115, 118, 121, 125, 125, 130, 135

Offset: 0

Benoit Cloitre, Mar 17 2003

			Pi truncated to 4 decimal places gives 3.1415 . The continued fraction for 3.1415 is [3, 7, 14, 1, 8, 2] which contains 6 terms, hence a(3)=6.

Cf. A065019.

cp's OEIS Frontend

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.

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