The On-Line Encyclopedia of Integer Sequences (OEIS)

A006839 revision #35

A006839

Minimum of largest partial quotient of continued fraction for k/n, (k,n) = 1.
(Formerly M0164)

1, 1, 1, 2, 1, 4, 2, 1, 3, 2, 2, 2, 1, 3, 2, 3, 2, 2, 2, 4, 1, 3, 3, 2, 2, 2, 2, 4, 2, 2, 2, 3, 3, 1, 3, 3, 2, 4, 3, 2, 2, 4, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 5, 1, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 1, 3, 2, 3, 2, 3, 3, 4, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2

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OFFSET

1,4

COMMENTS

Consider the continued fraction [0,c_1,c_2,...,c_m] of k/n, with k<n, c_m=1, and gcd(k,n)=1. Let f(k,n) be the maximum of the c_i. Then a(n) is the minimum value of f(k,n). This differs from A141822 only in the requirement that c_m=1. - Sean A. Irvine, Aug 12 2017

REFERENCES

Jeffrey Shallit, personal communication.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Robin Visser, Table of n, a(n) for n = 1..10000

H. Niederreiter, Dyadic fractions with small partial quotients, Monat. f. Math., 101 (1986), 309-315.

CROSSREFS

Cf. A141822.

Sequence in context: A013942 A187816 A088423 * A268267 A205395 A367647

Adjacent sequences: A006836 A006837 A006838 * A006840 A006841 A006842

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from David W. Wilson

STATUS

approved