login
A262216
Minimum number of 6's such that n*[n; 6, ..., 6, n] = [x; ..., x] for some x, where [...] denotes simple continued fractions.
2
1, 1, 3, 4, 1, 7, 7, 5, 9, 11, 3, 5, 7, 9, 15, 8, 5, 3, 19, 7, 11, 23, 7, 24, 5, 17, 7, 14, 9, 29, 31, 11, 17, 39, 11, 2, 3, 5, 39, 19, 7, 41, 11, 29, 23, 47, 15, 55, 49, 17, 11, 25, 17, 59, 7, 3, 29, 19, 19, 30, 29, 23, 63, 29, 11, 21, 35, 23, 39, 69, 23, 36, 5, 49, 3, 23, 5, 77
OFFSET
2,3
COMMENTS
Sequence A213895 lists fixed points of this sequence.
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[6, #] & /@ 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}
A262216(n, d=6)=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: A339278 A202500 A016607 * A076446 A053289 A076412
KEYWORD
nonn
AUTHOR
M. F. Hasler, Sep 15 2015
STATUS
approved