A376121 Continued fraction expansion of the real root of x^3 - 2*x^2 - 1.

2, 4, 1, 6, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 27, 1654, 1, 1, 6, 16, 7, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 3, 5, 3, 3, 1, 2, 3, 1, 2, 2, 197, 1, 8, 1, 1, 4, 1, 1, 3, 1, 5, 79, 1, 2, 1, 2, 15, 11, 2, 1, 3, 6, 4, 4, 17, 1, 12, 1, 1, 1, 1, 1, 1, 1, 3, 1, 7, 1, 1, 1, 1, 1, 7, 1, 2, 1, 6

Offset

0,1

Comments

This constant is called the supersilver ratio.

Links

Nicolas Boeglen, Table of n, a(n) for n = 0..10000

Wikipedia, Supersilver ratio.

Example

2 + 1/(4 + 1/(1 + 1/(6 + 1/(2 + ...)))) = 2.20556943040059031170202861...

Mathematica

ContinuedFraction[Root[#^3 - 2*#^2 - 1 &, 1], 100] (* Paolo Xausa, Oct 02 2024 *)

Crossrefs

Cf. A356035 (decimal expansion).

Sequence in context: A078886 A307796 A095247 * A007734 A171233 A362004

Adjacent sequences: A376118 A376119 A376120 * A376122 A376123 A376124

Keyword

nonn,cofr

Author

Nicolas Boeglen, Sep 11 2024

Status

approved