A189037 - OEIS

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A189037

Decimal expansion of (9-sqrt(17))/8.

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

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OFFSET

0,1

COMMENTS

Decimal expansion of the shape (= length/width = ((9-sqrt(17))/8) of the lesser (9/4)-contraction rectangle.

See A188738 for an introduction to lesser and greater r-contraction rectangles, their shapes, and partitioning these rectangles into a sets of squares in a manner that matches the continued fractions of their shapes.

LINKS

Table of n, a(n) for n=0..129.

EXAMPLE

0.60961179679779243127232376800324037185660009...

MATHEMATICA

r = 9/4; t = (r - (-4 + r^2)^(1/2))/2; FullSimplify[t]

N[t, 130]

RealDigits[N[t, 130]][[1]]

ContinuedFraction[t, 120]

RealDigits[(9-Sqrt[17])/8, 10, 150][[1]] (* Harvey P. Dale, Jan 30 2019 *)

CROSSREFS

Cf. A188738.