A006839 Minimum of largest partial quotient of continued fraction for k/n, (k,n) = 1.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Consider the continued fraction [0,c_1,c_2,...,c_m] of k/n, with kA141822 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.

Extensions

More terms from David W. Wilson