Let PD the sequence of the digital roots of {p(i)} (CD is defined similarly for {c(i)}):
PD = {2, 3, 5, 7, 2, 4, 8, 1, 5, 2, ...}
CD = {4, 6, 8, 9, 1, 3, 5, 6, 7, 9, ...}
Let Pn be the integer formed by concatenating the first n elements of PD (Cn is defined similarly for CD).
P10 = 2357248152
C10 = 4689135679
Let f(n) be the smallest positive integer that is a common superinteger of Pn and Cn. For example, f(10) = 2357246891352679, and f(100) mod 1000000007 = 771661825.