A331692 - OEIS

%I #27 Dec 22 2024 10:53:05

%S 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,

%T 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,

%U 1,1,36,1,2,1,1,1,2,3,2,1,3,3,31,2,1,2,2,2

%N Continued fraction for square root of golden ratio.

%H Kevin Ryde, <a href="/A331692/b331692.txt">Table of n, a(n) for n = 0..10000</a>

%H Kevin Ryde, <a href="/A331692/a331692.gp.txt">PARI/GP Code</a>

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

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

%o (PARI) contfrac(sqrt((1+sqrt(5))/2)) \\ _Michel Marcus_, Mar 04 2020

%o (PARI) \\ See Ryde link

%Y Cf. A001622, A139339 (decimal expansion).

%Y Cf. A225204/A225205 (convergents).

%K nonn,cofr

%O 0,2

%A _Jordan Paschke_, Mar 03 2020