The classic IQ test sequence "1, 3, 5, 7, ..." is typically solved by spotting the pattern "add 2 each time," making the next number 9. But this mathematician said "hold my coffee" and constructed an entire 4th-degree polynomial function that perfectly fits the first four points AND then produces 217341 as the fifth term!
This is actually mathematically valid - you can always find a polynomial of degree n-1 that passes through n points. It's called polynomial interpolation, and it's why mathematicians sometimes overthink "simple" pattern recognition problems. Their brains are wired to find the most elegant (or in this case, absurdly complex) solution that satisfies all constraints.
Next time someone asks you to continue a sequence, remember there are technically infinite correct answers. The simplest one is just boring!