A190180 - OEIS

%I #12 Sep 08 2022 08:45:56

%S 1,3,5,1,2,1,1,1,2,1,12,1,5,1,1,2,1,14,2,9,11,1,12,1,2,1,832,1,2,2,5,

%T 1,1,17,1,2,1,9,1,12,1,1,1,6,3,2,1,1,6,3,1,1,1,2,2,1,3,1,3,3,1,2,1,45,

%U 1,1,1,1,62,9,1,1,2,3,1,6,1,3,5,1

%N Continued fraction of (1+sqrt(-3+4*sqrt(2)))/2.

%C Equivalent to the periodic continued fraction [1,r,1,r,...] where r=1+sqrt(2), the silver ratio. For geometric interpretations of both continued fractions, see A189979 and A188635.

%C 1 followed by A190178.

%H G. C. Greubel, <a href="/A190180/b190180.txt">Table of n, a(n) for n = 1..10000</a>

%t r = 1 + 2^(1/2));

%t FromContinuedFraction[{1, r, {1, r}}]

%t FullSimplify[%]

%t ContinuedFraction[%, 100]  (* A190180 *)

%t RealDigits[N[%%, 120]]     (* A190179 *)

%t N[%%%, 40]

%t ContinuedFraction[(1 + Sqrt[-3 + 4*Sqrt[2]])/2, 100] (* _G. C. Greubel_, Dec 28 2017 *)

%o (PARI) contfrac((1+sqrt(-3+4*sqrt(2)))/2) \\ _G. C. Greubel_, Dec 28 2017

%o (Magma) ContinuedFraction((1+Sqrt(-3+4*Sqrt(2)))/2); // _G. C. Greubel_, Dec 28 2017

%Y Cf. A190179, A188635, A190177, A190178.

%K nonn,cofr

%O 1,2

%A _Clark Kimberling_, May 05 2011