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Term

Undulating Number

Numbers whose digits alternate between two values, ababab… (101, 121, 4747, 69696).

99 numbers tagged.

An undulating number has digits that bounce between two distinct values in an a-b-a-b pattern: 121, 484, 1717, 69696, 80808. The name evokes a wave. We require at least three digits and two different digits, so repdigits like 111 don't count.

The two-digit "seed" can be anything, giving families like 1010…, 1212…, 9090…. Undulating primes (an undulating number that's also prime, like 16361 or 1919191919191919191) are studied as a curiosity; it's known, for instance, that no undulating number with more than a handful of specific forms can be a perfect square.

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