  In this short note we look at the problem of counting juggling patterns with
one ball or two balls with a throw at every occurrence. We will do this for
both traditional juggling and for spherical juggling. In the latter case we
will show a connection to the "associated Mersenne numbers" (A001350) and so as
a result will be able to recover a proof that the $p$th Lucas number is
congruent to 1 modulo p when p is a prime.
