%I #34 Aug 09 2024 01:51:14

%S 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,

%T 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,

%U 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

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

%H G. C. Greubel, <a href="/A188804/b188804.txt">Table of n, a(n) for n = 0..999</a>

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

%p numtheory:-cfrac((Pi-sqrt(Pi^2-4))/2,40,'quotients'); # _Robert Israel_, Jun 15 2015

%t r = Pi; t = (r - (-4 + r^2)^(1/2))/2; FullSimplify[t]

%t N[t, 130]

%t RealDigits[N[t, 130]][[1]]

%t ContinuedFraction[t, 120]

%o (PARI) contfrac((Pi-sqrt(-4+Pi^2))/2) \\ _Michel Marcus_, Jun 14 2015

%Y Cf. A189044 (decimal expansion).

%K nonn,cofr

%O 0,2

%A _Clark Kimberling_, Apr 15 2011

%E Definition corrected by _Robert Israel_, Jun 15 2015

%E Offset changed by _Andrew Howroyd_, Aug 08 2024