On the parity of \(p(n)\). II (Q1208043)

\textit{O. Kolberg} [Math. Scand. 7, 377-378 (1960; Zbl 0091.044)] has proved that \(p(n)\) is infinitely often even, infinitely often odd. In part I, the author and \textit{M. V. Subbarao} [Acta Arith. 50, 355-356 (1988; Zbl 0657.10010)] have obtained the same result for \(p(16n+r)\) for every \(r\). Congruences modulo 2 for the generating functions of \(p(3n+r)\), \(r=0,1,2\), and of \(p(5n+r)\), \(r=0,1,2,3,4\), are now used to show that for every \(r\), \(p(12n+r)\) and \(p(40n+r)\) are each infinitely often even, infinitely often odd.