A289917 Decimal expansion of the limiting ratio of consecutive terms of A289916.

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

Offset

1,2

Links

Table of n, a(n) for n=1..86.

Formula

Equals (1 + sqrt(13) + sqrt(2*sqrt(13) - 2))/4. - Vaclav Kotesovec, Aug 27 2021

Largest real root of x^4 - x^3 - x^2 - x + 1. - Linas Vepstas, Feb 06 2024

Example

1.722083805739042245027069212153831462070116555...

Mathematica

z = 2000; r = 9/7;
u = CoefficientList[Series[1/Sum[Round[(k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}],
  x];  (* A289916  *)
v = N[u[[z]]/u[[z - 1]], 200]
RealDigits[v, 10][[1]] (* A289917 *)

Crossrefs

Cf. A078140 (includes guide to related constants), A289916.

Sequence in context: A274570 A334056 A176704 * A198415 A195723 A138996

Adjacent sequences: A289914 A289915 A289916 * A289918 A289919 A289920

Keyword

nonn,cons,easy

Author

Clark Kimberling, Jul 18 2017

Status

approved