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A189044
Decimal expansion of (Pi-sqrt(-4+Pi^2))/2.
2
3, 5, 9, 4, 3, 3, 0, 0, 3, 8, 1, 0, 2, 7, 7, 0, 8, 9, 1, 4, 6, 5, 4, 5, 3, 8, 7, 4, 4, 8, 2, 2, 0, 0, 1, 2, 2, 5, 5, 2, 6, 2, 9, 2, 1, 6, 1, 8, 7, 6, 6, 5, 1, 6, 4, 4, 1, 0, 1, 1, 6, 0, 8, 1, 8, 9, 6, 4, 8, 4, 8, 6, 4, 4, 7, 7, 3, 9, 0, 7, 2, 1, 2, 1, 5, 9, 2, 3, 3, 2, 4, 6, 3, 0, 4, 9, 1, 8, 0, 3, 3, 9, 2, 4, 9, 3, 5, 2, 9, 4, 0, 5, 0, 2, 8, 8, 4, 0, 9, 2, 6, 2, 3, 0, 9, 2, 3, 9, 5, 2
OFFSET
0,1
COMMENTS
Decimal expansion of the shape (= length/width = (Pi-sqrt(-4+Pi^2))/2) of the lesser pi-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.
FORMULA
Equals A000796 - A189039. - Alois P. Heinz, Jul 21 2022
EXAMPLE
0.3594330038102770891465453874482200...
MATHEMATICA
r = Pi; t = (r - (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
ContinuedFraction[t, 120]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Apr 15 2011
EXTENSIONS
Offset corrected by Alois P. Heinz, Jul 21 2022
STATUS
approved