Some folks just can. One of my former bosses called it "seeing the holes". One of the tests I had for hiring analysts was a visual test. "What do you see", helped tell me how people think.
Ya, I'd always say start at zero and tell me primes. then when they'd get to around 41 or 43, I'd say OK start at zero and tell me perfect numbers. The funny thing though is there can be a smart guy that doesn't
fall through the cracks. We hired a genius who was too lazy to hit a lick at a snake. He became obsessed about rewriting the standard qsort function. What a waste of brainpower. I'm sure he's pulling down a cool $60k at some university somewhere.