2nd powers and digital sums

Level 2

1 , 4 , 7 , 10 , 13 , 7 , 19 , 22 , 25 1,4,7,10,13,7,19,22,25

What number comes next?


The answer is 19.

Louis Ullman by Louis Ullman , 16, USA

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1 solution

Louis Ullman
Jun 23, 2018

The n n th number in the sequence is equal to the sum of the digits of the 2 ( n − 1 ) 2(n-1) th power of 2.

For example, the 1st number in the sequence is the sum of the digits of the 0th power of 2, the 2nd number in the sequence is the sum of the digits of the 2nd power of 2, etc.

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Great puzzle. However, you may want to consider changing the title to "... digital sums " because for the digital root you actually have to keep summing until the answer is a single digit; e.g. for 256, the digital sum would be 2 + 5 + 6 = 13, but the digital root would be 2 + 5 + 6 = 13, 1 + 3 = 4.

zico quintina - 2 years, 11 months ago

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