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%I #17 Jan 01 2023 17:48:14
%S 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 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 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 Decimal expansion of (5^(1/4) + 5^(3/4))/2.
%C 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 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.
%F Equals sqrt(A090550).
%e 2.419525153051665330964032180217076538651...
%t RealDigits[(Surd[5,4]+Surd[5^3,4])/2,10,120][[1]] (* _Harvey P. Dale_, Jan 01 2023 *)
%o (PARI) my(c=250+150*quadgen(20)); a_vector(len) = digits(sqrtint(floor(c*100^(len-2)))); \\ _Kevin Ryde_, May 28 2021
%Y Cf. A011003, A344362.
%K nonn,cons
%O 1,1
%A _Daniel Carter_, May 15 2021
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