

A262220


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


22



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
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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=#v1, 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 * A202252 A261633 A277103
Adjacent sequences: A262217 A262218 A262219 * A262221 A262222 A262223


KEYWORD

nonn


AUTHOR

M. F. Hasler, Sep 15 2015


STATUS

approved



