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A289915 Decimal expansion of the limiting ratio of consecutive terms of A289914. 2
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
KEYWORD
nonn,cons,easy
AUTHOR
Clark Kimberling, Jul 18 2017
STATUS
approved

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Last modified April 20 16:11 EDT 2024. Contains 371844 sequences. (Running on oeis4.)