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A262212 Minimum number of 2's such that n*[n; 2, ..., 2, n] = [x; ..., x] for some x, where [...] denotes simple continued fractions. 22

%I

%S 1,3,3,2,3,5,7,11,5,11,3,6,5,11,15,7,11,19,11,11,11,21,7,14,13,35,11,

%T 4,11,29,31,11,7,5,11,18,19,27,23,9,11,43,11,11,21,45,15,41,29,7,27,

%U 26,35,11,23,19,9,19,11,30,29,11,63,20,11,67,7,43,5,69,23,35,37,59,19,11,27,25,47,107,9,83,11,23,43,19,23,43,11,41,43,59,45,59,31

%N Minimum number of 2's such that n*[n; 2, ..., 2, n] = [x; ..., x] for some x, where [...] denotes simple continued fractions.

%C Sequence A213891 lists fixed points of this sequence.

%t f[m_, n_] := Block[{c, k = 1}, c[x_, y_] := ContinuedFraction[x FromContinuedFraction[Join[{x}, Table[m, {y}], {x}]]]; While[First@ c[n, k] != Last@ c[n, k], k++]; k]; f[2, #] & /@ Range[2, 120] (* _Michael De Vlieger_, Sep 16 2015 *)

%o (PARI) cf(v)={t=v[#v];forstep(i=#v-1,1,-1,t=v[i]+1/t);t}

%o A262212(n,d=2)=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, A262213 - A262220, A213900, A262211; A000057, A213891 - A213899, A261311.

%K nonn

%O 2,2

%A _M. F. Hasler_, Sep 15 2015

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Last modified May 10 21:08 EDT 2021. Contains 343780 sequences. (Running on oeis4.)