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A262218 Minimum number of 8's such that n*[n; 8, ..., 8, n] = [x; ..., x] for some x, where [...] denotes simple continued fractions. 2
1, 3, 1, 2, 3, 7, 1, 11, 5, 3, 3, 2, 7, 11, 3, 16, 11, 17, 5, 7, 3, 23, 3, 14, 5, 35, 7, 14, 11, 31, 7, 3, 33, 23, 11, 18, 17, 11, 5, 20, 7, 41, 3, 11, 23, 45, 3, 55, 29, 67, 5, 25, 35, 11, 7, 35, 29, 57, 11, 30, 31, 23, 15, 2, 3, 5, 33, 23, 23, 71, 11, 36, 37, 59, 17, 7, 11, 15, 11, 107, 41, 81, 7, 50, 41, 59, 3, 43, 11, 23, 23, 31, 45, 17, 7, 48, 55, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

Sequence A213897 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[8, #] & /@ 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}

A262218(n, d=8)=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: A060477 A175945 A209859 * A331695 A245538 A080890

Adjacent sequences:  A262215 A262216 A262217 * A262219 A262220 A262221

KEYWORD

nonn

AUTHOR

M. F. Hasler, Sep 15 2015

STATUS

approved

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Last modified May 9 19:47 EDT 2021. Contains 343746 sequences. (Running on oeis4.)