cp's OEIS Frontend

A188888 Continued fraction of sqrt(2 + sqrt(3)) or 2*cos(Pi/12).

%I A188888 #30 Aug 09 2024 01:53:09
%S A188888 1,1,13,1,2,15,10,1,18,1,1,21,2,1,1,2,4,5,2,2,2,11,1,2,2,3,1,1,10,1,2,
%T A188888 1,2,3,2,3,15,1,2,3,1,1,90,1,44,2,4,10,1,11,9,1,17,1,8,2,2,6,2,6,1,3,
%U A188888 1,1,1,2,20,1,7,27,1,19,40,1,304,1,1,2,1,1,1,62,1,1,2,1,2,1,32,1,1,1,11,1,20,1,85,1,1,1,3,3,13,1,4,1,3,1,3,1,16,1,9,3,2,1,1,30,2,1
%N A188888 Continued fraction of sqrt(2 + sqrt(3)) or 2*cos(Pi/12).
%C A188888 For a geometric interpretation, see A188640 and A188887.
%H A188888 G. C. Greubel, <a href="/A188888/b188888.txt">Table of n, a(n) for n = 0..9999</a>
%e A188888 sqrt(2+sqrt(3)) = [1,1,13,1,2,15,10,1,18,1,1,21,2,1,1,2,4,...].
%p A188888 with(numtheory): cfrac(sqrt(2+sqrt(3)),120,'quotients'); # _Muniru A Asiru_, Sep 30 2018
%t A188888 r = 2^(1/2); t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
%t A188888 N[t, 130]
%t A188888 RealDigits[N[t, 130]][[1]]
%t A188888 ContinuedFraction[t, 120]
%t A188888 ContinuedFraction[Sqrt[2+Sqrt[3]],120] (* _Harvey P. Dale_, Jul 19 2014 *)
%o A188888 (PARI) default(realprecision, 100); contfrac(sqrt(2 + sqrt(3))) \\ _G. C. Greubel_, Sep 29 2018
%o A188888 (Magma) SetDefaultRealField(RealField(100));  ContinuedFraction(Sqrt(2 + Sqrt(3))); // _G. C. Greubel_, Sep 29 2018
%Y A188888 Cf. A188887 (decimal expansion).
%K A188888 nonn,cofr
%O A188888 0,3
%A A188888 _Clark Kimberling_, Apr 12 2011
%E A188888 Name extended by _Greg Dresden_, Apr 13 2018
%E A188888 Offset changed by _Andrew Howroyd_, Aug 08 2024