A Diginacei 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.
A Diginacei 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.
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