A262220 Minimum number of 10's such that n*[n; 10, ..., 10, n] = [x; ..., x] for some x, where [...] denotes simple continued fractions.

1, 3, 3, 1, 3, 7, 7, 11, 1, 9, 3, 12, 7, 3, 15, 3, 11, 17, 3, 7, 9, 21, 7, 9, 25, 35, 7, 14, 3, 31, 31, 19, 3, 7, 11, 8, 17, 51, 7, 20, 7, 43, 19, 11, 21, 47, 15, 55, 9, 3, 51, 8, 35, 9, 7, 35, 29, 57, 3, 30, 31, 23, 63, 25, 19, 21, 3, 43, 7, 71, 23, 36, 17, 19, 35, 39, 51, 77, 15, 107, 41, 81, 7, 3, 43, 59, 39, 44, 11, 103, 43, 31, 47, 17, 31, 48, 55, 59

Offset

2,2

Comments

Sequence A213899 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[10, #] & /@ 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}
A262220(n, d=10)=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, A213891 - A213899; A262212 - A262219, A213900.

Sequence in context: A047655 A078685 A078882 * A325254 A202252 A261633

Adjacent sequences: A262217 A262218 A262219 * A262221 A262222 A262223

Keyword

nonn

Author

M. F. Hasler, Sep 15 2015

Status

approved