Neighbour Sequence

So far we find a set of coefficients \(s_k\) to generate a sequence via the above transform. We may also investigate the following sequence generated by those coefficients \[\sigma_k = \Prod_{l=1}^k s_l^{k-l+1}\]

we find for the greater twin primes the coefficients for the sequence \[5,35,112,576,1728,8640,...\]