A188804 Continued fraction for (Pi - sqrt(-4 + Pi^2))/2.

0, 2, 1, 3, 1, 1, 2, 3, 1, 4, 1, 1, 34, 4, 1, 3, 2, 1, 2, 2, 14, 1, 9, 5, 1, 1, 1, 1, 1, 9, 2, 1, 3, 2, 2, 2, 3, 26, 1, 8, 10, 2, 1, 23, 1, 67, 1, 2, 5, 1, 2, 3, 1, 1, 2, 1, 1, 17, 1, 2, 1, 9, 3, 8, 3, 3, 1, 2, 1, 21, 4, 1, 3, 1, 74, 1, 3, 1, 26, 1, 19, 1, 1, 2, 3, 1, 5, 1, 4, 2, 1, 2, 1, 2, 1, 1, 1, 1, 3, 4, 1, 1, 2, 1, 1, 1, 7, 1, 2, 38, 1, 9, 5, 6, 1, 1, 2, 1, 1, 4

Offset: 0

Author

Clark Kimberling, Apr 15 2011

Keywords

• nonn
• cofr

Examples

			(Pi - sqrt(-4 + Pi^2))/2 = [0,2,1,3,1,1,2,3,1,5,1,1,34,...].
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..999

Crossrefs

Cf. A189044 (decimal expansion).

Programs

Maple

numtheory:-cfrac((Pi-sqrt(Pi^2-4))/2,40,'quotients'); # Robert Israel, Jun 15 2015

Mathematica

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

PARI

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

Extensions

Definition corrected by Robert Israel, Jun 15 2015

Offset changed by Andrew Howroyd, Aug 08 2024