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 The first term of a sequence is 13. Starting with the second term, each term is the sum of the cubes of the digits in the previous term. For example, the second term is 1^3 + 3^3 = 28. Find the 5th term.

 Jun 22, 2022
 #1
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Third term =  2^3 + 8^3 =  520

Fourth term =  5^3 + 2^3 + 0^3   =  133

Fifth term =  1^3 + 3^3 + 3^3 =  55

 

 

Note an interesting thing

Sixth term  =  5^3 + 5^3    =  250

Seventh term =  2^3 + 5^3 + 0^3  =  133

 

So.....starting with the fourth term , the series repeats in a  cycle of three terms

 

cool cool cool

 Jun 22, 2022
 #2
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+1

13, 28, 520, 133, 55

 

For problems like these, we only have 5 terms to calculate. Therefore, brute forcing would be a convenient method

 Jun 22, 2022

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