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.
%I A344363 #19 Jun 24 2024 11:26:54
%S A344363 2,4,1,9,5,2,5,1,5,3,0,5,1,6,6,5,3,3,0,9,6,4,0,3,2,1,8,0,2,1,7,0,7,6,
%T A344363 5,3,8,6,5,1,8,1,7,8,5,7,9,3,8,5,4,7,0,8,4,6,8,3,2,5,5,3,8,2,8,9,5,8,
%U A344363 8,4,0,4,2,5,3,9,8,9,9,6,8,5,7,3,5,8,0,1,5,5,0,8,2,4,1,8,4,6,7,8,4,8,7,3,8
%N A344363 Decimal expansion of (5^(1/4) + 5^(3/4))/2.
%C A344363 Solution for z in the system {x = 1/y + 1/z, y = x + 1/z, z = y + 1/x}. The corresponding values of x and y are (5^(1/4) + 5^(-1/4))/2 and 5^(1/4).
%C A344363 The largest aspect ratio of a set of three rectangles which have the property that any two of them can be scaled, rotated, and joined at an edge to obtain a rectangle with the third aspect ratio. The other two aspect ratios are given in the comment above.
%H A344363 I. J. Zucker, G. S. Joyce, <a href="https://doi.org/10.1017/S0305004101005254">Special values of the hypergeometric series II</a>, Math. Proc. Cam. Phil. Soc. 131 (2001) 309 eq (8.8)
%F A344363 Equals sqrt(A090550).
%F A344363 Equals Gamma(1/20)*Gamma(9/20)/(Gamma(3/20)*Gamma(7/20)). [Zucker] - _R. J. Mathar_, Jun 24 2024
%e A344363 2.419525153051665330964032180217076538651...
%t A344363 RealDigits[(Surd[5,4]+Surd[5^3,4])/2,10,120][[1]] (* _Harvey P. Dale_, Jan 01 2023 *)
%o A344363 (PARI) my(c=250+150*quadgen(20)); a_vector(len) = digits(sqrtint(floor(c*100^(len-2)))); \\ _Kevin Ryde_, May 28 2021
%Y A344363 Cf. A011003, A344362.
%K A344363 nonn,cons
%O A344363 1,1
%A A344363 _Daniel Carter_, May 15 2021