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Decimal expansion of the continued fraction with elements given by A209272.
0

%I #17 Jul 02 2023 02:00:32

%S 1,6,4,4,9,4,8,6,5,0,1,1,5,9,5,7,5,6,0,9,6,0,7,7,9,4,5,0,9,7,8,5,8,0,

%T 9,1,5,8,6,3,2,9,5,3,4,9,6,4,6,6,4,3,8,7,5,9,3,7,0,2,7,6,9,2,1,4,9,2,

%U 3,3,6,0,1,6,3,1,8,4,4,2,4,8,4,6,0,7,0,6,8,1,1,7,9,0,0,2,8,6,7,0,8

%N Decimal expansion of the continued fraction with elements given by A209272.

%C The numerator and the denominator of the n-th convergent for this number are always squarefree. Close to zeta(2) = 1.644934066848...

%o (PARI) /* realprecision = 202 significant digits */ v=[1];for(k=1,200,m=1;while(issquarefree(contfracpnqn(concat(v,[m]))[1,1])+issquarefree(contfracpnqn(concat(v,[m]))[2,1])<2,m++);v=concat(v,[m]);print((contfracpnqn(v)[1,1])*1./(contfracpnqn(v)[2,1]),""))

%Y Cf. A209272.

%K nonn,cons

%O 1,2

%A _Benoit Cloitre_, Jan 15 2013