A189090 Continued fraction of Pi + sqrt(Pi^2 - 1).

6, 8, 2, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 2, 6, 1, 14, 2, 1, 6, 3, 1, 1, 2, 3, 7, 1, 1, 3, 2, 2, 1, 3, 10, 1, 1, 4, 3, 3, 10, 1, 2, 2, 18, 3, 77, 1, 1, 18, 1, 2, 2, 4, 1, 2, 8, 1, 4, 1, 44, 1, 28, 1, 4, 1, 1, 2, 116, 1, 1, 2, 2, 1, 5, 4, 5, 27, 4, 1, 3, 1, 3, 5, 1, 2, 2, 1, 16, 1, 3, 1, 5, 2, 1, 1, 25, 3, 1, 1, 17, 1, 5, 3, 1, 2, 1, 4, 12, 4, 7, 42, 19, 1, 2, 23, 1, 3, 2, 1, 4

Offset: 0

Author

Clark Kimberling, Apr 16 2011

Keywords

• nonn
• cofr

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A189089, A189088.

Programs

Mathematica

r = 2*Pi; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
N[t, 130]
RealDigits[N[t, 130]][[1]] (*A189089*)
ContinuedFraction[t, 120]  (*A189090*)

PARI

contfrac(Pi+sqrt(Pi^2-1)) \\ Charles R Greathouse IV, Jul 29 2011