

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
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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=#v1, 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



