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

Author

Jordan Paschke, Mar 03 2020

Keywords

• nonn
• cofr

Examples

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

Links

• Kevin Ryde, Table of n, a(n) for n = 0..10000
• Kevin Ryde, PARI/GP Code

Crossrefs

Cf. A001622, A139339 (decimal expansion).

Cf. A225204/A225205 (convergents).

Programs

Mathematica

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

PARI

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

PARI

\\ See Ryde link