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 A262220 Minimum number of 10's such that n*[n; 10, ..., 10, n] = [x; ..., x] for some x, where [...] denotes simple continued fractions. 22
 1, 3, 3, 1, 3, 7, 7, 11, 1, 9, 3, 12, 7, 3, 15, 3, 11, 17, 3, 7, 9, 21, 7, 9, 25, 35, 7, 14, 3, 31, 31, 19, 3, 7, 11, 8, 17, 51, 7, 20, 7, 43, 19, 11, 21, 47, 15, 55, 9, 3, 51, 8, 35, 9, 7, 35, 29, 57, 3, 30, 31, 23, 63, 25, 19, 21, 3, 43, 7, 71, 23, 36, 17, 19, 35, 39, 51, 77, 15, 107, 41, 81, 7, 3, 43, 59, 39, 44, 11, 103, 43, 31, 47, 17, 31, 48, 55, 59 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS Sequence A213899 lists fixed points of this sequence. LINKS MATHEMATICA 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[10, #] & /@ Range[2, 120] (* Michael De Vlieger, Sep 16 2015 *) PROG (PARI) cf(v)={t=v[#v]; forstep(i=#v-1, 1, -1, t=v[i]+1/t); t} A262220(n, d=10)=for(k=1, 9e9, (c=contfrac(cf(vector(k+2, i, if(i>1&&i

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Last modified April 22 19:11 EDT 2021. Contains 343177 sequences. (Running on oeis4.)