a(0) = 1, a(n) = k*a(n-1) + 1 is a multiple of n-th prime. If no such number exists then a(n) = 0 and a(n+1) = k*a(n-1) + 1 is a multiple of (n+1)-th prime; i.e., a(r) = smallest multiple of the r-th prime = k* a(s) + 1 where a(s) is the last nonzero term.

A069565

a(0) = 1, a(n) = k*a(n-1) + 1 is a multiple of n-th prime. If no such number exists then a(n) = 0 and a(n+1) = k*a(n-1) + 1 is a multiple of (n+1)-th prime; i.e., a(r) = smallest multiple of the r-th prime = k* a(s) + 1 where a(s) is the last nonzero term.