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.

A089078 Continued fraction for sqrt(2) + sqrt(3).

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%I A089078 #20 Aug 17 2019 17:49:28
%S A089078 3,6,1,5,7,1,1,4,1,38,43,1,3,2,1,1,1,1,2,4,1,4,5,1,5,1,7,22,2,5,1,1,2,
%T A089078 1,1,31,2,1,1,3,1,44,1,89,1,8,5,2,5,1,1,4,2,8,1,17,1,4,3,4,3,2,1,1,4,
%U A089078 2,1,9,1,15,13,1,39,20,2,152,3,2,4,1,30,1,3,1,2,1,2,16,3,24,1,9,1,172,3,1,1
%N A089078 Continued fraction for sqrt(2) + sqrt(3).
%C A089078 This is the most natural example of the fact that the sum of two periodic continued fractions need not have a periodic continued fraction.
%C A089078 a(n) is the numbers of squares removed at stage n of the continued-fraction partitioning of a rectangle of length L and width W satisfying W=L*sqrt(8); see A188640. - _Clark Kimberling_, Apr 13 2011
%H A089078 G. C. Greubel, <a href="/A089078/b089078.txt">Table of n, a(n) for n = 0..5000</a>
%H A089078 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%t A089078 r = 8^(1/2); t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t]
%t A089078 N[t, 130]
%t A089078 RealDigits[N[t, 130]][[1]]
%t A089078 ContinuedFraction[t, 120]
%t A089078 ContinuedFraction[Sqrt[2]+Sqrt[3],100] (* _Harvey P. Dale_, Aug 17 2019 *)
%o A089078 (PARI) contfrac(sqrt(2)+sqrt(3)) \\ _Michel Marcus_, Mar 12 2017
%Y A089078 Cf. A135611.
%K A089078 cofr,nonn
%O A089078 0,1
%A A089078 _Jeppe Stig Nielsen_, Dec 04 2003