A289915 Decimal expansion of the limiting ratio of consecutive terms of A289914.

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

Offset

1,2

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

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

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

Example

1.883203505913525864168947465362055090560951328672239179570777...

Mathematica

z = 2000; r = 7/5;
u = CoefficientList[Series[1/Sum[Round[(k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}],
  x];  (* A289914  *)
v = N[u[[z]]/u[[z - 1]], 200]
RealDigits[v, 10][[1]] (* A289915 *)
First[RealDigits[(1 + Sqrt[2] + Sqrt[2*Sqrt[2] - 1])/2, 10, 100]] (* Paolo Xausa, Feb 08 2024 *)

Crossrefs

Cf. A078140 (includes guide to related constants), A289914.

Sequence in context: A265292 A272415 A010530 * A021535 A371466 A199188

Adjacent sequences: A289912 A289913 A289914 * A289916 A289917 A289918

Keyword

nonn,cons,easy

Author

Clark Kimberling, Jul 18 2017

Status

approved