A190261 Continued fraction of (1 + sqrt(1 + 2x))/2, where x=sqrt(2).

1, 2, 11, 32, 1, 4, 10, 2, 1, 1, 3, 1, 1, 5, 2, 3, 2, 1, 4, 2, 3, 2, 41, 1, 2, 1, 1, 3, 4, 1, 35, 1, 5, 1, 29661, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 5, 2, 2, 2, 1, 1, 1, 5, 15, 2, 1, 1, 1, 2, 7, 1, 1, 1, 13, 1, 1, 1, 1, 20, 2, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 3, 14, 1, 8, 2, 1, 1, 1, 1, 2, 1, 3, 2, 3, 1, 8, 2

Offset: 1

Author

Clark Kimberling, May 06 2011

Keywords

• nonn
• cofr

Comments

1 followed by A190259.

Links

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

Crossrefs

Cf. A190260, A190259.

Programs

Magma

ContinuedFraction((1+Sqrt(1+2*Sqrt(2)))/2) // G. C. Greubel, Dec 26 2017

Mathematica

r=2^(1/2);
FromContinuedFraction[{1, r, {1, r}}]
FullSimplify[%]
ContinuedFraction[%, 100]  (* A190261 *)
RealDigits[N[%%, 120]]     (* A190260 *)
N[%%%, 40]
ContinuedFraction[(1+Sqrt[1+2Sqrt[2]])/2,100] (* Harvey P. Dale, Jan 27 2013 *)

PARI

contfrac((1+sqrt(1+2*sqrt(2)))/2) \\ G. C. Greubel, Dec 26 2017