A344363 Decimal expansion of (5^(1/4) + 5^(3/4))/2.

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

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

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

I. J. Zucker, G. S. Joyce, Special values of the hypergeometric series II, Math. Proc. Cam. Phil. Soc. 131 (2001) 309 eq (8.8)

Formula

Equals sqrt(A090550).

Equals Gamma(1/20)*Gamma(9/20)/(Gamma(3/20)*Gamma(7/20)). [Zucker] - R. J. Mathar, Jun 24 2024

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

Cf. A011003, A344362.

Sequence in context: A097607 A132893 A273896 * A163240 A091958 A372879

Adjacent sequences: A344360 A344361 A344362 * A344364 A344365 A344366

Keyword

nonn,cons

Author

Daniel Carter, May 15 2021

Status

approved