A262213 Minimum number of 3's such that n*[n; 3, ..., 3, n] = [x; ..., x] for some x, where [...] denotes simple continued fractions.

2, 1, 5, 2, 5, 7, 5, 5, 2, 3, 5, 12, 23, 5, 11, 7, 5, 19, 5, 7, 11, 21, 5, 14, 38, 17, 23, 6, 5, 31, 23, 3, 23, 23, 5, 18, 59, 25, 5, 6, 23, 41, 11, 5, 65, 47, 11, 55, 14, 7, 77, 25, 17, 11, 23, 19, 20, 11, 5, 29, 95, 23, 47, 38, 11, 67, 23, 21, 23, 71, 5, 36, 56, 29, 59, 7, 77, 25, 11, 53

Offset: 2

Author

M. F. Hasler, Sep 15 2015

Keywords

• nonn

Comments

Sequence A213892 lists fixed points of this sequence.

Crossrefs

Cf. A213648, A262212 - A262220, A213900, A262211; A000057, A213891 - A213899, A261311.

Programs

PARI

cf(v)={t=v[#v];forstep(i=#v-1,1,-1,t=v[i]+1/t);t}
A262213(n,d=3)=for(k=1,9e9,(c=contfrac(cf(vector(k+2,i,if(i>1&&i