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A344363 Decimal expansion of (5^(1/4) + 5^(3/4))/2. 1
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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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).
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.
LINKS
FORMULA
Equals sqrt(A090550).
EXAMPLE
2.419525153051665330964032180217076538651...
MATHEMATICA
RealDigits[(Surd[5, 4]+Surd[5^3, 4])/2, 10, 120][[1]] (* Harvey P. Dale, Jan 01 2023 *)
PROG
(PARI) my(c=250+150*quadgen(20)); a_vector(len) = digits(sqrtint(floor(c*100^(len-2)))); \\ Kevin Ryde, May 28 2021
CROSSREFS
Sequence in context: A097607 A132893 A273896 * A163240 A091958 A372879
KEYWORD
nonn,cons
AUTHOR
Daniel Carter, May 15 2021
STATUS
approved

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Last modified June 19 07:40 EDT 2024. Contains 373492 sequences. (Running on oeis4.)