A262215 Minimum number of 5's such that n*[n; 5, ..., 5, n] = [x; ..., x] for some x, where [...] denotes simple continued fractions.

2, 3, 5, 1, 11, 5, 5, 3, 5, 11, 11, 2, 5, 3, 11, 8, 11, 19, 5, 11, 11, 21, 11, 9, 2, 3, 5, 28, 11, 31, 23, 11, 8, 5, 11, 18, 59, 11, 5, 6, 11, 43, 11, 3, 65, 47, 11, 41, 29, 35, 5, 12, 11, 11, 5, 19, 86, 57, 11, 30, 95, 11, 47, 5, 11, 65, 17, 43, 5, 69, 11, 36, 56, 19, 59, 11, 11, 79, 11, 11, 20, 81, 11, 17, 131, 115, 11, 44, 11, 5, 65, 31, 47, 19, 23, 48

Offset

2,1

Comments

Sequence A213894 lists fixed points of this sequence.

Links

Table of n, a(n) for n=2..97.

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[5, #] & /@ 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}
A262215(n, d=5)=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: A030335 A256611 A276350 * A030790 A001578 A262341

Adjacent sequences: A262212 A262213 A262214 * A262216 A262217 A262218

Keyword

nonn

Author

M. F. Hasler, Sep 15 2015

Status

approved