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%I #7 Sep 16 2015 09:23:56
%S 2,1,5,2,5,7,5,5,2,3,5,12,23,5,11,7,5,19,5,7,11,21,5,14,38,17,23,6,5,
%T 31,23,3,23,23,5,18,59,25,5,6,23,41,11,5,65,47,11,55,14,7,77,25,17,11,
%U 23,19,20,11,5,29,95,23,47,38,11,67,23,21,23,71,5,36,56,29,59,7,77,25,11,53
%N Minimum number of 3's such that n*[n; 3, ..., 3, n] = [x; ..., x] for some x, where [...] denotes simple continued fractions.
%C Sequence A213892 lists fixed points of this sequence.
%o (PARI) cf(v)={t=v[#v];forstep(i=#v-1,1,-1,t=v[i]+1/t);t}
%o A262213(n,d=3)=for(k=1,9e9,(c=contfrac(cf(vector(k+2,i,if(i>1&&i<k+2,d,n)))*n))[1]==c[#c]&&return(k))
%Y Cf. A213648, A262212 - A262220, A213900, A262211; A000057, A213891 - A213899, A261311.
%K nonn
%O 2,1
%A _M. F. Hasler_, Sep 15 2015
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