cp's OEIS Frontend

A188728 Continued fraction of (e+sqrt(16+e^2))/4.

%I A188728 #17 Aug 09 2024 01:50:54
%S A188728 1,1,7,1,46,8,30,1,5,4,2,6,3,2,5,1,1,1,3,50,1,3,1,1,3,1,45,1,1,1,4,1,
%T A188728 1,2,8,2,35,2,1,27,6,112,1,113,16,1,11,1,1,6,1,12,1,3,2,15,1,2,1,1,5,
%U A188728 1,16,2,2,2,1,10,1,43,1,13,1,6,1,4,1,2,1,1,1,6,1,8,8,1,6,3,3,17,3,1,27,1,11,1,1,1,1,1,1,9,7,2,1,5,5,7,6,2,1,5,1,2,1,5,57,8,2,1
%N A188728 Continued fraction of (e+sqrt(16+e^2))/4.
%C A188728 See A188727 for the origin of the constant.
%H A188728 G. C. Greubel, <a href="/A188728/b188728.txt">Table of n, a(n) for n = 0..9999</a>
%e A188728 (e+sqrt(16+e^2))/4 = [1,1,7,1,46,30,1,5,4,...].
%t A188728 r = e/2; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
%t A188728 N[t, 130]
%t A188728 RealDigits[N[t, 130]][[1]] (* A188727 *)
%t A188728 ContinuedFraction[t, 120] (* A188728 *)
%o A188728 (PARI) default(realprecision, 100); contfrac((exp(1) + sqrt(16 + exp(2)))/4) \\ _G. C. Greubel_, Oct 31 2018
%o A188728 (Magma) SetDefaultRealField(RealField(100)); ContinuedFraction((Exp(1)  + Sqrt(16 + Exp(2)))/4); // _G. C. Greubel_, Oct 31 2018
%Y A188728 Cf. A188640, A188727 (decimal expansion).
%K A188728 nonn,cofr
%O A188728 0,3
%A A188728 _Clark Kimberling_, Apr 10 2011
%E A188728 Offset changed by _Andrew Howroyd_, Aug 08 2024