strict partitions into catalans and powers of 3

[Meeussen Wouter (bkarnd)]

> Any number can be so partitioned in at least one way. (true?) 
***False***
> the following numbers can be so partitioned in one way only:
>
1,2,4,7,13,21,40,63,121,195,364,624,1093,1353,1794,2054,3280,3540,3981,4
241,
> 4710,5486,5955,6215

The first stretch (length 38) of stictly unpartitionables begins after
16757 =
q[1]q[2]q[5]q[14]q[42]q[132]q[429]q[1430]q[4862]r[3]r[9]r[27]r[81]r[243]
r[729]r[2187]r[6561]
and ends with
16796 = q[16796]

and a second stretch (also length 38) begins after
36440=
q[1]q[2]q[5]q[14]q[42]q[132]q[429]q[1430]q[4862]r[3]r[9]r[27]r[81]r[243]
r[729]r[2187]r[6561]r[19683]
and ends with
36479 = q[16796]r[19683]

my apologies to those of you, specially Roland Bacher, who might have
been wrongfooted.

W.

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