3, 3, 5, 4, 4, 3, 5, 5, 4, 3, what next?

Question

Find the rule and the next term of 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, ? Do not look for an arithmetic pattern; there is none. Once you have the rule, give the three terms after the missing one as well, and name a second famous sequence built on the same kind of idea.

Accepted Answer

The next term is 6. Each term is the number of letters in the English name of the counting numbers: one, two, three, four, five, six, seven, eight, nine, ten, eleven. Check. One (3), two (3), three (5), four (4), five (4), six (3), seven (5), eight (5), nine (4), ten (3), and eleven (6). After that: twelve (6), thirteen (8), fourteen (8), fifteen (7). Why it stumps people. Interview sequence puzzles are usually numerical, so solvers try differences, ratios and primes before considering that the numbers might be counting something outside mathematics. When a sequence is bounded and jumps aroun…

3, 3, 5, 4, 4, 3, 5, 5, 4, 3, what next?

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