Explain the pattern and find the next five rows.

Hint: the symbols I chose have nothing to do with the pattern.

That seems good to me. For the entries that are not a power of a prime, what could we have? Look at 6:

6 +===+=

To me this looks like "2==2", which has 3 terms (+=, ==, +=). And 6 has 2 and 3 as its only factors.

This also works with 10:

+=+===+=+= would be 22==22, 5 terms total, and 10=2*5. So possible answers for 14 and 15 would be:

14 +=+=+===+=+=+=
15 ++=++====++=++=

or 15 might possibly be:

15 ++=++===++=++=

depending on whether the separator is === or == in this case.

But I'm not really happy with this, and have no idea what would happen when you get to 30 (the first number with 3 distinct primes in its factorization)

Posted by Brian Wainscott on 2004-02-20 15:11:27