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.

A190264 Decimal expansion of (sqrt(89) - 6)/2.

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%I A190264 #15 Dec 26 2017 23:36:58
%S A190264 1,7,1,6,9,9,0,5,6,6,0,2,8,3,0,1,9,0,5,6,6,0,3,3,0,1,8,8,8,1,1,3,2,0,
%T A190264 3,5,8,4,9,1,8,1,1,3,1,6,7,0,7,5,6,0,6,6,0,3,3,1,4,9,0,7,2,4,4,9,0,0,
%U A190264 1,1,4,5,4,7,9,2,5,5,9,0,2,9,2,7,0,5,1,3,4,9,3,4,4,5,1,9,2,0,5,2,2,6,7,5,0,6,4,8,7,1,4,0,8,7,4,9,3,7,4,9
%N A190264 Decimal expansion of (sqrt(89) - 6)/2.
%C A190264 The rectangle R whose shape (i.e., length/width) is (-6 + sqrt(89))/2 can be partitioned into rectangles of shapes 3/2 and 3 in a manner that matches the periodic continued fraction [3/2, 3, 3/2, 3, ...].  R can also be partitioned into squares so as to match the periodic continued fraction [1, 1, 2, 1, 1, 6, 1, 36, 1, 6, 1, 1, 2, 1, 8, 1, 2, 1, 1, 6, 1, 36, ...].  For details, see A188635.
%C A190264 Quadratic number with denominator 2 and minimal polynomial 4x^2 + 24x - 53. - _Charles R Greathouse IV_, Apr 21 2016
%H A190264 G. C. Greubel, <a href="/A190264/b190264.txt">Table of n, a(n) for n = 1..10000</a>
%e A190264 1.716990566028301905660330188811320358491...
%t A190264 FromContinuedFraction[{3/2, 3, {3/2, 3}}]
%t A190264 ContinuedFraction[%, 100]  (* [1, 1, 2, 1, 1, 6, 1, 36, ... *)
%t A190264 RealDigits[N[%%, 120]]     (* A190264 *)
%t A190264 N[%%%, 40]
%o A190264 (PARI) sqrt(89)/2-3 \\ _Charles R Greathouse IV_, Apr 21 2016
%Y A190264 Cf. A188635, A190290, A178255.
%K A190264 nonn,cons
%O A190264 1,2
%A A190264 _Clark Kimberling_, May 07 2011