2, 3, 10, 12, 13, 20, 21, 22, what next?

Question

Find the rule and the next term of 2, 3, 10, 12, 13, 20, 21, 22, ? There is no arithmetic pattern. Say the numbers out loud, and once you have the rule, explain why 11 and 14 to 19 are missing and what the first term above 39 will be.

Accepted Answer

The next term is 23. These are the whole numbers whose English names begin with the letter T, in increasing order. Check. Two, three, ten, twelve, thirteen, twenty, twenty-one, twenty-two, twenty-three, and then twenty-four up to twenty-nine, thirty, thirty-one, ... Note what is skipped: eleven (E), fourteen to nineteen (F, S, E, N), and everything from 40 to 199 (forty, fifty, sixty, seventy, eighty, ninety, one hundred). The thirties all start with T, so the sequence runs 30 to 39 and then jumps straight to 200 (two hundred). How to spot it. Bounded, irregular, no differences or ratios of n…

2, 3, 10, 12, 13, 20, 21, 22, what next?

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