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I'm trying to understand the formula presented for the sequence A064532 from the OEIS, looks like a recurrence relation with complex numbers:

$a(10i+j) = a(i) + a(j), etc.$

Sorry if its a simple equation, but I wasn't able to understand it.

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up vote 2 down vote accepted

Nothing to do with complex numbers.

Look at the number of holes in each digit

0 1 2 3 4 5 6 7 8 9
1 0 0 0 0 0 1 0 2 1

Now look at the total number of holes when you write the number in the usual way; just take the weighted sum of the digits.

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Ok, so if I understood there is no "closed form" formula for a formula like a(8) = 2 for instance, right ? – Tarantulae Apr 4 '12 at 17:10
Sorry my answer did not typeset properly. The digit 8 has two holes; just look at it. There is no formula for the number of holes in a digit. – Bruce Westbury Apr 4 '12 at 17:30
You will kick yourself when you get it! or as my children would say "facepalm"! – Bruce Westbury Apr 4 '12 at 17:38
Thanks Bruce ! hheeh – Tarantulae Apr 4 '12 at 17:44
Edited only to align the table (insert quadruple space before each line). But it looks to me like the digit 9 has one hole, not zero.$$ $$I'm reminded of the GRE question I heard of last week(?): Which of the following shapes is simple connected? (A)a (B)b (C)c (D)d (E)e – Noam D. Elkies Apr 4 '12 at 17:55

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