

A189088


Decimal expansion of Pi  sqrt(Pi^2  1).


3



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

0,2


COMMENTS

Decimal expansion of the shape (= length/width = Pi  sqrt(1+Pi^2)) of the lesser 2*Picontraction rectangle.
See A188738 for an introduction to lesser and greater rcontraction rectangles, their shapes, and partitioning these rectangles into a sets of squares in a manner that matches the continued fractions of their shapes.


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000


EXAMPLE

0.1634045465204364424868140709760745094117386882...


MATHEMATICA

r = 2*Pi; t = (r  (4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]] (* A189088 *)
ContinuedFraction[t, 120]
RealDigits[PiSqrt[Pi^21], 10, 150][[1]] (* Harvey P. Dale, Sep 25 2016 *)


PROG

(PARI) Pi*(1sqrt(11/Pi^2)) \\ Charles R Greathouse IV, May 07, 2011


CROSSREFS

Cf. A188738, A189089, A189090.
Sequence in context: A108661 A117042 A227989 * A195301 A196824 A309988
Adjacent sequences: A189085 A189086 A189087 * A189089 A189090 A189091


KEYWORD

nonn,easy,cons


AUTHOR

Clark Kimberling, Apr 16 2011


STATUS

approved



