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Question from bharat, a student:

if
1=5
2=25
3=325
4=4325
5=?

Bharat,

1 : 5
2 : 25
3 : 325
4 : 4325
5 : ?????

The first term is 5. Starting with the second term, what is the first digit of each successive term? What should be the first digit of the fifth term?

Penny

 

I don't know. (The improper use of the equals sign here doesn't make it any easier.)

I don't see any pattern simpler than continuing 54325, 654325, etc, though it's a bit arbitrary & what the 10th term is to be is unclear. The fourth term is not an integer multiple of the third, breaking one obvious pattern.

Prime factorizations are 5, 5*5, 5*5*13, 5*5*173. I do note that
5 = 12 + 4, 13 = 32 + 4, 173 = 132 + 4 but as 3 never appears anywhere this is probably not useful either.

Good Hunting!
RD

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