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.

A190181 Decimal expansion of (15+sqrt(465))/12.

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%I A190181 #10 Sep 08 2022 08:45:56
%S A190181 3,0,4,6,9,8,8,2,2,1,0,7,0,6,5,2,0,5,6,2,2,7,8,2,8,4,8,3,2,5,0,0,9,8,
%T A190181 7,2,9,8,0,7,0,8,8,3,6,0,9,7,5,6,5,8,1,6,9,6,1,0,9,4,1,7,1,0,4,7,6,3,
%U A190181 1,1,1,7,8,1,0,5,7,1,6,9,9,8,9,2,9,5,0,4,3,6,8,7,8,2,3,8,3,4,1,4,2,6,6,9,7,3,2,7,0,4,4,1,3,0,0,1,0,3,1,3
%N A190181 Decimal expansion of (15+sqrt(465))/12.
%C A190181 The rectangle R whose shape (i.e., length/width) is (15+sqrt(465))/12 can be partitioned into rectangles of shapes 5/2 and 3/2 in a manner that matches the periodic continued fraction [5/2, 3/2, 5/2, 3/2,...]. R can also be partitioned into squares so as to match the periodic continued fraction [3,21,3,1,1,4,1,4,1,1,3,21,...]. For details, see A188635.
%H A190181 G. C. Greubel, <a href="/A190181/b190181.txt">Table of n, a(n) for n = 1..10000</a>
%e A190181 3.046988221070652056227828483250098729807...
%t A190181 FromContinuedFraction[{5/2, 3/2, {5/2, 3/2}}]
%t A190181 FullSimplify[%]
%t A190181 ContinuedFraction[%, 100]  (* [3,21,3,1,1,4,1,4,1,1,3,21,...] *)
%t A190181 RealDigits[N[%%, 120]]      (* A190181 *)
%t A190181 N[%%%, 40]
%t A190181 RealDigits[(15+Sqrt[465])/12, 10, 100][[1]] (* _G. C. Greubel_, Dec 28 2017 *)
%o A190181 (PARI) (15+sqrt(465))/12 \\ _G. C. Greubel_, Dec 28 2017
%o A190181 (Magma) [(15+sqrt(465))/12]; // _G. C. Greubel_, Dec 28 2017
%Y A190181 Cf. A188635.
%K A190181 nonn,cons
%O A190181 1,1
%A A190181 _Clark Kimberling_, May 05 2011