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A262212 Minimum number of 2's such that n*[n; 2, ..., 2, n] = [x; ..., x] for some x, where [...] denotes simple continued fractions. 22
1, 3, 3, 2, 3, 5, 7, 11, 5, 11, 3, 6, 5, 11, 15, 7, 11, 19, 11, 11, 11, 21, 7, 14, 13, 35, 11, 4, 11, 29, 31, 11, 7, 5, 11, 18, 19, 27, 23, 9, 11, 43, 11, 11, 21, 45, 15, 41, 29, 7, 27, 26, 35, 11, 23, 19, 9, 19, 11, 30, 29, 11, 63, 20, 11, 67, 7, 43, 5, 69, 23, 35, 37, 59, 19, 11, 27, 25, 47, 107, 9, 83, 11, 23, 43, 19, 23, 43, 11, 41, 43, 59, 45, 59, 31 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

Sequence A213891 lists fixed points of this sequence.

LINKS

Table of n, a(n) for n=2..96.

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[2, #] & /@ 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}

A262212(n, d=2)=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, A262213 - A262220, A213900, A262211; A000057, A213891 - A213899, A261311.

Sequence in context: A129309 A268931 A003560 * A123676 A326814 A122775

Adjacent sequences:  A262209 A262210 A262211 * A262213 A262214 A262215

KEYWORD

nonn

AUTHOR

M. F. Hasler, Sep 15 2015

STATUS

approved

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Last modified April 22 19:11 EDT 2021. Contains 343177 sequences. (Running on oeis4.)