A188723 - OEIS

%I #11 Jul 07 2024 12:24:59

%S 3,2,3,4,2,3,1,1,105,1,2,1,13,5,16,1,44,1,1,4,2,1,2,3,100,4,1,1,18,4,

%T 2,2,2,8,2,5,2,2,3,7,184,1,8,6,2,6,2,1,5,1,38,1,2,1,1,1,4,2,6,2,1,1,1,

%U 1,2,3,1,1,1,1,2,1,2,3,8,1,1,2,1,3,1,2,1,10,1,6,1,3,1,1,1,1,2,2,1,7,1,11,1,6,1,2,13,35,1,5,2,2,1,1,2,8,2,6,2,3,1,1,2,5

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

%C Continued fraction of the constant in A188722.

%p Digits := 100 ;

%p (Pi+sqrt(4+Pi^2))/2 ;

%p evalf(%) ;

%p numtheory[cfrac](%,40,'quotients') ; # _R. J. Mathar_, Apr 11 2011

%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]

%Y Cf. A000796, A188640, A188722 (decimal expansion).

%K nonn,cofr

%O 0,1

%A _Clark Kimberling_, Apr 09 2011

%E Offset changed by _Andrew Howroyd_, Jul 07 2024