A281112 - OEIS

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A281112

Decimal expansion of (conjectured) limit c(n+1)/c(n), where c = A078140.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

Clark Kimberling, Another question about the golden ratio and other numbers, MathOverflow, Jan 17 2017.

EXAMPLE

c(n+1)/c(n)) -> 1.688924110769165206686359... (conjectured)

MATHEMATICA

z = 3880; r = GoldenRatio;

f[x_] := f[x] = Sum[Floor[r*(k + 1)] x^k, {k, 0, z}];

t = CoefficientList[Series[1/f[x], {x, 0, z}], x]; (* A078140 *)