Let $f(n)=1+x^n+x^{2n}+...+x^{n^2}.$

Let $p(x)$ be $1+x+x^2+x^5+x^7+...$ where the exponents are the pentagonal numbers.

Let $a(n)$ be the sequence of integers such that the coefficients of the series $f(a(1)) f(a(2)) f(a(3))...$ are congruent mod $2$ to the coefficients of $p(x)$

The first few values of $a(n)$ are: $1,2,3,5,6,7,9,11,12,13,15,17,19,21,23,25,27$.

Describe the sequence a(1),a(2),a(3),...