

A188715


Minimal largest k in set of n fractions of the form (k1)/k all of whose ratios (smaller fraction / larger fraction) are also of that form.


0




OFFSET

1,1


COMMENTS

These ratios, together with 1, can be the constant speeds of cyclists going forever around a circular track while only allowed to pass each other at a single point.
For all n, a(n+1)<a(n)^(2n), so the series is infinite. [John Tromp, Apr 13 2011]


LINKS

Table of n, a(n) for n=1..10.


EXAMPLE

All pairwise ratios in the set {5/6,4/5,3/4,2/3} are also of the form (k1)/k, while for the only "lesser" size4 set {4/5,3/4,2/3,1/2}, we have (1/2)/(4/5)=5/8 is not of that form. So a(4)=6.


PROG

(Haskell)
let ext (c, l) = [(tails.filter(\b>a*(a1)`mod`(ba)==0)$r, a:l)  (a:r)<c] in map (last.snd.head) . tail . iterate (>>= ext) $ [(map reverse (inits[2..]), [])]
 for greater efficiency, replace map reverse (inits[2..]) by
 [m:[mdd<divisors(m*(m1)), d<m1]m<[2..]], defining divisors appropriately.


CROSSREFS

Sequence in context: A066463 A073146 A038767 * A174046 A095991 A293714
Adjacent sequences: A188712 A188713 A188714 * A188716 A188717 A188718


KEYWORD

nonn,more


AUTHOR

John Tromp, Apr 08 2011


EXTENSIONS

Finally found a(11); about the square of a(10). I doubt if a(12) will ever be found.


STATUS

approved



