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A262219 Minimum number of 9's such that n*[n; 9, ..., 9, n] = [x; ..., x] for some x, where [...] denotes simple continued fractions. 2
2, 1, 5, 4, 5, 5, 5, 1, 14, 11, 5, 6, 5, 9, 11, 16, 5, 17, 29, 5, 11, 21, 5, 24, 20, 5, 5, 14, 29, 31, 23, 11, 50, 29, 5, 17, 17, 13, 29, 2, 5, 43, 11, 9, 65, 47, 11, 41, 74, 33, 41, 26, 5, 59, 5, 17, 14, 57, 29, 30, 95, 5, 47, 34, 11, 67, 101, 21, 29, 7, 5, 35, 17, 49, 17, 11, 41, 79, 59, 17, 2, 3, 5, 84, 131, 29, 11, 43, 29, 41, 65, 31, 47, 89, 23, 7, 41 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
Sequence A213898 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[9, #] & /@ 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}
A262219(n, d=9)=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))
CROSSREFS
Cf. A000057, A213891 - A213899, A261311: fixed points of the above.
Sequence in context: A010582 A266628 A283441 * A249905 A171175 A176053
KEYWORD
nonn
AUTHOR
M. F. Hasler, Sep 15 2015
STATUS
approved

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Last modified March 2 05:08 EST 2024. Contains 370460 sequences. (Running on oeis4.)