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%I #17 Oct 02 2022 22:57:37
%S 2,7,8,2,1,5,9,6,4,9,7,7,9,5,1,6,1,4,9,3,1,6,0,9,7,9,9,5,8,3,1,2,8,2,
%T 8,7,1,9,4,1,9,0,6,4,7,7,7,5,6,3,3,9,3,0,4,5,3,3,9,3,2,9,8,4,1,1,8,1,
%U 6,7,9,1,9,8,3,8,4,6,9,9,2,6,5,0,6,4,4,2,4,9,2,8,7,9,0,6,7,8,8,7,6,4,2,8,9,8,7,3,3,5,7,2,7,7,9,4,2,2,5,5,4,4,7,0,7,5,2,2,1,4
%N Decimal expansion of (Pi+sqrt(-4+Pi^2))/2.
%C Decimal expansion of the shape (= length/width = (Pi+sqrt(-4+Pi^2))/2) of the greater Pi-contraction rectangle.
%C 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.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals A000796-A189044. - _Alois P. Heinz_, Jul 21 2022
%e 2.78215964977951614931609799583128287194190...
%t r = Pi; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
%t N[t, 130]
%t RealDigits[N[t, 130]][[1]] (*A189039*)
%t ContinuedFraction[t, 120] (*A188804*)
%o (PARI) (Pi+sqrt(-4+Pi^2))/2 \\ _Michel Marcus_, Jun 14 2015
%Y Cf. A000796, A188738, A188804, A189044.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Apr 16 2011