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A265289 Decimal expansion of Sum{c(2n) - x, n=1,2,...}, where c = convergents to (x = golden ratio). 3
4, 3, 8, 7, 5, 1, 4, 1, 0, 9, 7, 1, 5, 0, 6, 2, 5, 7, 3, 5, 5, 6, 4, 9, 5, 3, 9, 3, 4, 7, 5, 2, 7, 1, 9, 0, 1, 6, 9, 6, 6, 4, 1, 9, 3, 4, 2, 5, 9, 2, 0, 0, 6, 7, 1, 9, 4, 1, 3, 7, 2, 8, 5, 1, 5, 0, 3, 7, 2, 1, 9, 5, 3, 9, 9, 5, 9, 3, 2, 4, 5, 5, 0, 7, 4, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Define the upper deviance of x > 0 by dU(x) = sum{c(2n,x) - x), n=1,2,...}, where c(k,x) = k-th convergent to x.  The greatest upper deviance occurs when x = golden ratio, so that the constant in A265289 is the absolute maximal upper deviance.

LINKS

Table of n, a(n) for n=0..85.

EXAMPLE

sum = 0.4387514109715062573556495393475271901...

MATHEMATICA

x = GoldenRatio; z = 600; c = Convergents[x, z];

s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]

s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]

N[s1 + s2, 200]

RealDigits[s1, 10, 120][[1]]  (* A265288 *)

RealDigits[s2, 10, 120][[1]]  (* A265289 *)

RealDigits[s1 + s2, 10, 120][[1]] (* A265290 *)

CROSSREFS

Cf. A265288, A265290.

Sequence in context: A117956 A241638 A110662 * A302258 A132021 A089368

Adjacent sequences:  A265286 A265287 A265288 * A265290 A265291 A265292

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Dec 06 2015

STATUS

approved

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Last modified February 16 09:04 EST 2019. Contains 320159 sequences. (Running on oeis4.)