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Minimum of largest partial quotient of continued fraction for k/n, (k,n) = 1.
(Formerly M0164)
2

%I M0164 #35 Nov 01 2023 18:30:44

%S 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,

%T 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,

%U 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

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

%C 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

%D Jeffrey Shallit, personal communication.

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

%H Robin Visser, <a href="/A006839/b006839.txt">Table of n, a(n) for n = 1..10000</a>

%H H. Niederreiter, <a href="http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002485222">Dyadic fractions with small partial quotients</a>, Monat. f. Math., 101 (1986), 309-315.

%Y Cf. A141822.

%K nonn

%O 1,4

%A _N. J. A. Sloane_

%E More terms from _David W. Wilson_