A190264 - OEIS

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A190264

Decimal expansion of (sqrt(89) - 6)/2.

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

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OFFSET

1,2

COMMENTS

The rectangle R whose shape (i.e., length/width) is (-6 + sqrt(89))/2 can be partitioned into rectangles of shapes 3/2 and 3 in a manner that matches the periodic continued fraction [3/2, 3, 3/2, 3, ...]. R can also be partitioned into squares so as to match the periodic continued fraction [1, 1, 2, 1, 1, 6, 1, 36, 1, 6, 1, 1, 2, 1, 8, 1, 2, 1, 1, 6, 1, 36, ...]. For details, see A188635.

Quadratic number with denominator 2 and minimal polynomial 4x^2 + 24x - 53. - Charles R Greathouse IV, Apr 21 2016

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

EXAMPLE

1.716990566028301905660330188811320358491...

MATHEMATICA

FromContinuedFraction[{3/2, 3, {3/2, 3}}]

ContinuedFraction[%, 100] (* [1, 1, 2, 1, 1, 6, 1, 36, ... *)

RealDigits[N[%%, 120]] (* A190264 *)

N[%%%, 40]

PROG

(PARI) sqrt(89)/2-3 \\ Charles R Greathouse IV, Apr 21 2016