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Continued fraction of (1+sqrt(1+e^2))/e.
1

%I #8 Jul 08 2024 10:39:47

%S 1,2,3,3,1,15,1,3,7,1,2,4,2,1,4,1,1,12,4,52,1,2,1,7,3,6,1,21,1,11,1,4,

%T 1,3,2,3,2,7,1,1,2,1,3,2,1,43,4,1,1,4,4,18,2,4,4,2,1,2,3,1,3,9,1,9,4,

%U 1,6,1,1,1,2,10,1,1,1,1,2,1,2,1,2,21,2,2,1,4,1,3,12,1,9,6,1,1,4,5,2,1,1,1,1,3,1,3,16,1,6,3,10,1,8,1,8,1,13,21,1,2,4,1

%N Continued fraction of (1+sqrt(1+e^2))/e.

%C For a geometric interpretation, see A188640 and A188885.

%e (1+sqrt(1+e^2))/e=[1,2,3,3,1,15,1,3,7,1,2,4,...].

%t r = 2/E; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]

%t N[t, 130]

%t RealDigits[N[t, 130]][[1]]

%t ContinuedFraction[t, 120]

%Y Cf. A188640, A188885 (decimal expansion).

%K nonn,cofr

%O 0,2

%A _Clark Kimberling_, Apr 12 2011

%E Offset changed by _Andrew Howroyd_, Jul 08 2024