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I'm searching way to designate the last $n$ digits of the sum $i^i$.

I using this http://oeis.org/A001923/b001923.txt

And I noticed one fact.

The nine and ten words have identical digits, for example:

9 405071317

10 10405071317

19 2018612200059554303215024

20 106876212200059554303215024

How can I find similar dependencies?

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    The difference between the 9th and 10th terms is $10^{10}$, right? – 2017-02-20

1 Answers 1

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Well, $10^{10}$, $20^{20}$, and more generally $10k^{10k}$ are numbers which end in a lot of zeroes ($10k$ to be precise). So it makes sense that if you add them to the previous sum, some of the last digits are identical.

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    basically I want to designate n-last digits, but this numbers are too big – 2017-02-20
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    This relationship happens only on multiples of 10; otherwise, you won't find anything 'interesting'. – 2017-02-20
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    I'm grateful for your help – 2017-02-20