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A262215 Minimum number of 5's such that n*[n; 5, ..., 5, n] = [x; ..., x] for some x, where [...] denotes simple continued fractions. 2
2, 3, 5, 1, 11, 5, 5, 3, 5, 11, 11, 2, 5, 3, 11, 8, 11, 19, 5, 11, 11, 21, 11, 9, 2, 3, 5, 28, 11, 31, 23, 11, 8, 5, 11, 18, 59, 11, 5, 6, 11, 43, 11, 3, 65, 47, 11, 41, 29, 35, 5, 12, 11, 11, 5, 19, 86, 57, 11, 30, 95, 11, 47, 5, 11, 65, 17, 43, 5, 69, 11, 36, 56, 19, 59, 11, 11, 79, 11, 11, 20, 81, 11, 17, 131, 115, 11, 44, 11, 5, 65, 31, 47, 19, 23, 48 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Sequence A213894 lists fixed points of this sequence.

LINKS

Table of n, a(n) for n=2..97.

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[5, #] & /@ 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}

A262215(n, d=5)=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: A030335 A256611 A276350 * A030790 A001578 A262341

Adjacent sequences:  A262212 A262213 A262214 * A262216 A262217 A262218

KEYWORD

nonn

AUTHOR

M. F. Hasler, Sep 15 2015

STATUS

approved

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Last modified May 10 22:16 EDT 2021. Contains 343780 sequences. (Running on oeis4.)