A Diginacci sequence is created as follows. • The first two terms are any positive whole numbers. • Each of the remaining terms is the sum of the digits of the previous two terms. For example, starting with 5 and 8 the Diginacci sequence is 5, 8, 13, 12, 7, 10, ... The calculations for this example are 5 + 8 = 13, 8 + 1 + 3 = 12, 1+3+1+2=7, 1 + 2 + 7 = 10. a) Calculate the first 28 terms of the Diginacci sequence with starting terms 1 and 1, and then find the 2021st number in the sequence.
b) Show that if both starting terms in a Diginacci sequence are each less than one million, then its fourth and fifth terms are each less than 100.
c) Show that if both starting terms in a Diginacci sequence are each less than 100, then it has a term after which all terms are at most 20.
d) Show that if both starting terms in a Diginacci sequence are each less than 100, then it has a term after which all terms equal 18 or all terms are less than 18.