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

Author

Clark Kimberling, Jul 18 2017

Keywords

• nonn
• cons
• easy

Examples

			1.722083805739042245027069212153831462070116555...
		

Crossrefs

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

Programs

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 *)

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