A189971 Continued fraction of (1 + x + sqrt(14 + 10*x))/4, where x=sqrt(5).

2, 3, 6, 3, 1, 2, 15, 2, 3, 6, 1, 7, 1, 4, 2, 3, 1, 4, 2, 1, 1, 1, 2, 1, 20, 17, 3, 1, 2, 3, 1, 1, 3, 1, 4, 9, 73, 1, 37, 192, 3, 1, 1, 1, 1, 5, 1, 21, 1, 6, 7, 1, 3, 3, 1, 8, 2, 2, 1, 1, 8, 1, 2, 1, 1, 8, 1, 2, 1, 20, 2, 16, 3, 19, 2, 1, 3, 7, 1, 1, 2, 1, 2, 3, 1, 1, 1, 2, 9, 32, 1, 1, 10, 5, 1, 7, 5, 1, 1, 1

Offset: 1

Author

Clark Kimberling, May 05 2011

Keywords

• nonn
• cofr

Comments

Equivalent to the periodic continued fraction [r,1,r,1,...] where r=(1+sqrt(5))/2, the golden ratio. For geometric interpretations of both continued fractions, see A189970 and A188635.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001622, A189970, A188635, A190157, A190158.

Programs

Magma

ContinuedFraction( (1 + Sqrt(5) + Sqrt(14 + 10*Sqrt(5)) )/4 ); // G. C. Greubel, Jan 12 2018

Mathematica

(See A189970.)
ContinuedFraction[(1+Sqrt[5]+Sqrt[14+10Sqrt[5]])/4,120] (* Harvey P. Dale, Jul 31 2013 *)

PARI

contfrac((1+sqrt(5)+sqrt(14+10*sqrt(5)))/4) \\ G. C. Greubel, Jan 12 2018