Parity of number of partitions of an integer

[John Conway]

On Wed, 3 Sep 2003, Brendan McKay wrote:

> Is there a formula for the parity of the number of partitions
> of an integer?  It is A040051.

   This is an old question, to which nobody seems to have found even
a partial answer - a bit surprising in view of the fact that there 
are simple infinite sequences of numbers for which we know the
value of  p(n)  modulo 5 or 7 or 11.

      John Conway