OFFSET
1,1
COMMENTS
Apart from the first digit, the same as A171417. Apart from the first 2 digits, the same as A188734. - R. J. Mathar, Apr 15 2011
Decimal expansion of the shape (= length/width = (9+sqrt(65))/4) of the greater (9/2)-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.
EXAMPLE
4.2655644370746374130916533075759427827835990...
MATHEMATICA
r = 9/2; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]]
RealDigits[(9+Sqrt[65])/4, 10, 150][[1]] (* Harvey P. Dale, Jan 31 2023 *)
PROG
(PARI) (9+sqrt(65))/4 \\ Jinyuan Wang, Apr 14 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Apr 14 2011
STATUS
approved