A344362 Decimal expansion of (5^(1/4) + 5^(-1/4))/2.

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

Offset: 1

Author

Daniel Carter, May 15 2021

Keywords

• nonn
• cons

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.

Examples

			1.082044543098821282957566033699780665875...
		

Crossrefs

Cf. A011003, A344363, A293409, A176015.

Programs

Mathematica

RealDigits[Cosh[Log[5]/4], 10, 120][[1]] (* Amiram Eldar, Jun 29 2023 *)

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^(len-2)))); \\ Kevin Ryde, May 28 2021

Formula

Equals 5*A293409.

Equals sqrt(A176015).

Equals cosh(log(5)/4). - Vaclav Kotesovec, May 28 2021