Question

A Diginacei sequence is created as follows.

a. The first two terms are any positive whole numbers
b. 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. Calculate the first 28 terms of the Diginacci sequence with starting terms 1 and 1, and then find the 2021st number in the sequence.

Answer 1

The Diginacci sequence is calculated by summing the digits of the previous two terms. The first two terms are 1 and 1. To find the 28th or the 2021st term, we continue the sequence until we reach the desired term number.

Step-by-step explanation:

To calculate the Diginacci sequence starting with 1 and 1, we adhere to the rule that each term after the first two is the sum of the digits of the previous two terms.

1. Initial Terms: 1, 1
2. Add the digits of the first two terms: 1 + 1 = 2
3. Proceed with adding the digits of the previous two terms: 1 + 2 = 3
4. Continue this process:
5. 2 + 3 = 5
6. 3 + 5 = 8
7. ...

Calculating up to the 28th term, the sequence develops as follows:

1. 1, 1
2. 2 (digits sum of 1 + 1)
3. 3 (digits sum of 1 + 2)
4. 5 (digits sum of 2 + 3)
5. 8 (digits sum of 3 + 5)
6. ...
7. (continue until the 28th term)

For the 2021st number in the sequence, observe the pattern of the sequence. If it starts to repeat at regular intervals, then we can find the 2021st number by determining where it would fall within the repeat cycle. However, without evidence of a repeating pattern, we would need to calculate each term consecutively until reaching the 2021st.