A356035 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A356035

Decimal expansion of the real root of x^3 - 2*x^2 - 1.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

This is the minimum number having the property that there are uncountably many permutation classes with the growth rate equal to that number. [Vatter] - Andrey Zabolotskiy, Dec 04 2024

LINKS

Table of n, a(n) for n=1..88.

Vincent Vatter, Small permutation classes, Proc. London Math. Soc. (3), 103 (2011), 879-921; arXiv:0712.4006 [math.CO], 2007-2016.

Wikipedia, Supersilver ratio.

Index entries for algebraic numbers, degree 3

FORMULA

Equals ((172 + 12*sqrt(177))^(1/3)+16/(172 + 12*sqrt(177))^(1/3) + 4)/6.

Equals ((172 + 12*sqrt(177))^(1/3) + (172 - 12*sqrt(177))^(1/3) + 4)/6.

Equals (((1/2)*(43 + 3*sqrt(3*59)))^(1/3) + ((1/2)*(43 - 3*sqrt(3*59)))^(1/3) + 2)/3.

Equals 2*(1 + 2*cosh(log((43 + 3*sqrt(177))/16)/3))/3. - Vaclav Kotesovec, Aug 19 2022

Equals y + 2/3 where y = 1.538902... is the real root of y^3 - (4/3)*y - 43/27.

Equals 1 + A137421. - R. J. Mathar, Sep 23 2022