A189039 Decimal expansion of (Pi+sqrt(-4+Pi^2))/2.

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, 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, 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

Offset: 1

Author

Clark Kimberling, Apr 16 2011

Keywords

• nonn
• cons

Comments

Decimal expansion of the shape (= length/width = (Pi+sqrt(-4+Pi^2))/2) of the greater 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.

Examples

			2.78215964977951614931609799583128287194190...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A000796, A188738, A188804, A189044.

Programs

Mathematica

r = Pi; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]] (*A189039*)
ContinuedFraction[t, 120]  (*A188804*)

PARI

(Pi+sqrt(-4+Pi^2))/2 \\ Michel Marcus, Jun 14 2015

Formula

Equals A000796-A189044. - Alois P. Heinz, Jul 21 2022