A262216 Minimum number of 6's such that n*[n; 6, ..., 6, n] = [x; ..., x] for some x, where [...] denotes simple continued fractions.

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.

Links

Table of n, a(n) for n=2..79.

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. A213648, A262212 - A262220, A213900, A262211.

Cf. A000057, A213891 - A213899, A261311: fixed points of the above.

Sequence in context: A339278 A202500 A016607 * A076446 A053289 A076412

Adjacent sequences: A262213 A262214 A262215 * A262217 A262218 A262219

Keyword

nonn

Author

M. F. Hasler, Sep 15 2015

Status

approved