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%I #14 May 12 2022 23:07:05
%S 1,2,2,5,31,498,8955,2882938,52586050459,323804423976901335,
%T 15495775772522155664701173463,
%U 4775184376703288469595772730789093950647769107,365485679191762741290548194655325571866478457308489227548407339087759232157
%N Numerator of f(n), where for n > 2, f(n) = (n-1)/f(n-1) + (n-2)/f(n-2), with f(1)=1, f(2)=2.
%C f(n)-> sqrt(2n), a slowly converging sequence.
%C The next term in the sequence (a(14)) has 120 digits. - _Harvey P. Dale_, Nov 29 2011
%e f(3) = 2/f(2) + 1/f(1) = 2/2 + 1/1 = 2/1, so a(3) = 2.
%t Numerator[RecurrenceTable[{a[1]==1,a[2]==2,a[n]==(n-1)/a[n-1]+(n-2)/ a[n-2]},a,{n,13}]] (* _Harvey P. Dale_, Nov 29 2011 *)
%o (Maxima)
%o a[1]:1$
%o a[2]:2$
%o a[n]:=(n-1)/a[n-1]+(n-2)/a[n-2];
%o makelist(ratnumer(a[n]),n,1,15); /* _Martin Ettl_, Oct 30 2012 */
%Y Cf. A076659.
%K nonn,frac
%O 1,2
%A _Zak Seidov_, Oct 24 2002
%E One more term from _Harvey P. Dale_, Nov 29 2011
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