

A344362


Decimal expansion of (5^(1/4) + 5^(1/4))/2.


1



1, 0, 8, 2, 0, 4, 4, 5, 4, 3, 0, 9, 8, 8, 2, 1, 2, 8, 2, 9, 5, 7, 5, 6, 6, 0, 3, 3, 6, 9, 9, 7, 8, 0, 6, 6, 5, 8, 7, 5, 7, 4, 7, 4, 7, 4, 6, 3, 3, 5, 9, 1, 9, 5, 5, 1, 4, 3, 2, 8, 8, 4, 7, 6, 5, 9, 8, 3, 4, 5, 3, 9, 5, 2, 9, 7, 1, 7, 8, 7, 4, 2, 2, 8, 6, 6, 1, 0, 0, 8, 0, 4, 4, 7, 8, 3, 2, 3, 2, 5, 9, 3, 0, 3, 4
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OFFSET

1,3


COMMENTS

Solution for x in the system {x = 1/y + 1/z, y = x + 1/z, z = y + 1/x}. The corresponding values of y and z are 5^(1/4) and (5^(1/4) + 5^(3/4))/2.
The smallest 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

Table of n, a(n) for n=1..105.


FORMULA

Equals 5*A293409.
Equals sqrt(A176015).
Equals cosh(log(5)/4).  Vaclav Kotesovec, May 28 2021


EXAMPLE

1.082044543098821282957566033699780665875...


PROG

(PARI) solve(x=1, 2, 5*x^4  5*x^2  1) \\ Hugo Pfoertner, May 16 2021
(PARI) my(c=50+30*quadgen(20)); a_vector(len) = digits(sqrtint(floor(c*100^(len2)))); \\ Kevin Ryde, May 28 2021


CROSSREFS

Cf. A011003, A344363, A293409, A176015.
Sequence in context: A021850 A197576 A277313 * A182170 A011105 A098829
Adjacent sequences: A344359 A344360 A344361 * A344363 A344364 A344365


KEYWORD

nonn,cons


AUTHOR

Daniel Carter, May 15 2021


STATUS

approved



