A262217 Minimum number of 7's such that n*[n; 7, ..., 7, n] = [x; ..., x] for some x, where [...] denotes simple continued fractions.

2, 3, 5, 2, 11, 1, 5, 11, 2, 9, 11, 5, 5, 11, 11, 3, 11, 19, 5, 3, 29, 7, 11, 2, 5, 35, 5, 6, 11, 31, 23, 19, 11, 5, 11, 8, 59, 11, 5, 20, 11, 13, 29, 11, 23, 45, 11, 13, 2, 3, 5, 52, 35, 29, 5, 19, 20, 57, 11, 30, 95, 11, 47, 5, 59, 67, 11, 7, 5, 23, 11, 36, 8, 11, 59, 9, 11, 79, 11, 107, 20, 27, 11, 11, 41, 27, 29, 43, 11, 5, 23, 31, 137, 59, 23, 47, 41, 59

Offset

2,1

Comments

Sequence A213896 lists fixed points of this sequence.

Links

Table of n, a(n) for n=2..99.

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[7, #] & /@ 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}
A262217(n, d=7)=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: A355091 A137826 A021429 * A124055 A137458 A079369

Adjacent sequences: A262214 A262215 A262216 * A262218 A262219 A262220

Keyword

nonn

Author

M. F. Hasler, Sep 15 2015

Status

approved