A188884 Continued fraction of (1 + sqrt(1 + Pi^2))/Pi.
1, 2, 1, 2, 1, 1, 3, 1, 1, 5, 1, 7, 1, 1, 23, 2, 2, 4, 3, 1, 11, 158, 1, 1, 1, 1, 4, 2, 1, 6, 2, 19, 75, 1, 1, 1, 28, 1, 29, 6, 8, 1, 5, 1, 4, 2, 1, 8, 1, 1, 19, 1, 1, 9, 2, 2, 3, 1, 2, 11, 1, 1, 3, 1, 1, 4, 169, 1, 1, 2, 1, 3, 1, 1, 10, 2, 1, 3, 8, 2, 4, 8, 5, 1, 8, 1, 7, 1, 1, 1, 1, 4, 38, 1, 5, 1, 43, 1, 1, 1, 1, 2, 1, 8, 1, 20, 1, 1, 1, 2, 13, 51, 2, 21, 1, 2, 5, 1, 1, 1
Offset: 0
Examples
(1 + sqrt(1 + Pi^2))/Pi = [1, 2, 1, 2, 1, 1, 3, 1, 1, 5, 1, 7, 1, 1, 23, 2, ...].
Programs
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Mathematica
r = 2/Pi; t = (r + (4 + r^2)^(1/2))/2; FullSimplify[t] N[t, 130] RealDigits[N[t, 130]][[1]] ContinuedFraction[t, 120] ContinuedFraction[(1+Sqrt[1+Pi^2])/Pi,120] (* Harvey P. Dale, May 02 2025 *)
Extensions
Offset changed by Andrew Howroyd, Jul 07 2024
Comments