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%I #20 Dec 24 2020 21:25:12
%S 1,1,1,1,2,5,13,19,58,191,655,1187,4462,17519,71063,149405,646846,
%T 2887921,13237457,31166057,150303170,742458253,3748521653,9670072483,
%U 50903810666,273315477775,1495006933759,4163946939067,23599037077934
%N Denominator of c(n) where c(0)=1 c(n+1) = n/c(n) + 1.
%C Dvornicich et al proved that c(n) is an integer only for n<4, so that a(n)=1 only for n<4. - _Michel Marcus_, Dec 24 2020
%H Roberto Dvornicich, Francesco Veneziano, and Umberto Zannier, <a href="http://arxiv.org/abs/1403.3470">On the integral values of a curious recurrence</a>, arXiv:1403.3470 [math.NT], 2014.
%H <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.
%F It seems that log(a(n)) is asymptotic to C*n*Log(n) with C=0.4....
%t Denominator[RecurrenceTable[{c[1]==1,c[n]==(n-1)/c[n-1]+1},c,{n,30}]] (* _Harvey P. Dale_, Jun 11 2013 *)
%o (PARI) lista(nn) = {my(x = 1); for (n=0, nn, print1(denominator(x), ", "); x = 1+ n/x;);} \\ _Michel Marcus_, Dec 24 2020
%Y Cf. A072898.
%K easy,frac,nonn
%O 0,5
%A _Benoit Cloitre_, Aug 10 2002
%E a(0)=1 prepended by _Michel Marcus_, Dec 24 2020
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