cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A188658 Decimal expansion of (1+sqrt(101))/10.

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%I A188658 #26 Jul 04 2023 03:28:03
%S A188658 1,1,0,4,9,8,7,5,6,2,1,1,2,0,8,9,0,2,7,0,2,1,9,2,6,4,9,1,2,7,5,9,5,7,
%T A188658 6,1,8,6,9,4,5,0,2,3,4,7,0,0,2,6,3,7,7,2,9,0,5,7,2,8,2,8,2,9,7,3,2,8,
%U A188658 4,9,1,2,3,1,5,5,1,9,7,0,3,8,1,2,3,6,1,7,7,6,9,2,4,5,3,9,5,2,3,5,2,3,6,6,2,9,9,5,0,3,2,6,5,2,6,1,3,2,3,1,8,8,1,5,9,3,5,8,5,7
%N A188658 Decimal expansion of (1+sqrt(101))/10.
%C A188658 Decimal expansion of the shape of a (1/5)-extension rectangle; see A188640 for definitions of shape and r-extension rectangle.  Briefly, shape=length/width, and an r-extension rectangle is composed of two rectangles of shape 1/r when r<1.
%C A188658 The continued fraction is 1, 9, 1, 1, 9, 1, 1, 9, 1, 1, 9, 1, 1, 9, 1...
%H A188658 Clark Kimberling, <a href="http://www.jstor.org/stable/27963362">A Visual Euclidean Algorithm</a>, The Mathematics Teacher 76 (1983) 108-109.
%F A188658 Equals exp(arcsinh(1/10)). - _Amiram Eldar_, Jul 04 2023
%e A188658 1.104987562112089027021926491275957618694502347002...
%t A188658 r = 1/5; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
%t A188658 N[t, 130]
%t A188658 RealDigits[N[t, 130]][[1]]
%t A188658 ContinuedFraction[t, 120]
%t A188658 RealDigits[(1+Sqrt[101])/10,10,150][[1]] (* _Harvey P. Dale_, Nov 29 2020 *)
%Y A188658 Cf. A188640.
%K A188658 nonn,cons
%O A188658 1,4
%A A188658 _Clark Kimberling_, Apr 10 2011
%E A188658 a(130) corrected by _Georg Fischer_, Apr 02 2020