Riddler Classic, July 3 2020

Got last week’s Express just right, with the right explanation.

This week’s Classic is based on the US flag, but the maths question is this:

[W]hen N equals 50, N is twice a square and N+1 is a centered pentagonal number. After 50, what is the next integer N with these properties?

This one seems very easy to brute force. My code returns an answer in less than a thousandth of a second. The returned answer is twice a square, and one less than a centred pentagonal. It’s definitely possible that I missed the correct, lower answer because there’s a mistake in my logic for stepping through the possible doubled squares and centred pentagonals.

I’m very curious to know if there’s a good way to solve this analytically.

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