A331692 Continued fraction for square root of golden ratio.

1, 3, 1, 2, 11, 3, 5, 1, 10, 1, 2, 5, 3, 5, 1, 2, 4, 1, 1, 2, 4, 51, 1, 4, 2, 2, 31, 1, 3, 1, 1, 5, 1, 1, 1, 14, 1, 1, 4, 2, 2, 8, 1, 1, 3, 23, 1, 1, 4, 16, 2, 1, 2, 13, 2, 1, 1, 1, 3, 1, 1, 4, 3, 2, 1, 1, 36, 1, 2, 1, 1, 1, 2, 3, 2, 1, 3, 3, 31, 2, 1, 2, 2, 2

Offset

0,2

Links

Kevin Ryde, Table of n, a(n) for n = 0..10000

Kevin Ryde, PARI/GP Code

Example

1 + 1/(3 + 1/(1 + 1/(2 + 1/(11 + ...)))) = sqrt(phi).

Mathematica

ContinuedFraction[Sqrt[(1 + Sqrt[5])/2], 1000]

Prog

(PARI) contfrac(sqrt((1+sqrt(5))/2)) \\ Michel Marcus, Mar 04 2020
(PARI) \\ See Ryde link

Crossrefs

Cf. A001622, A139339 (decimal expansion).

Cf. A225204/A225205 (convergents).

Sequence in context: A307665 A144156 A116854 * A016567 A304058 A305452

Adjacent sequences: A331689 A331690 A331691 * A331693 A331694 A331695

Keyword

nonn,cofr

Author

Jordan Paschke, Mar 03 2020

Status

approved