given one, three, five, seven, nine (odd numbers), seems like the machine should have said "there are no odd numbers without an e" since every odd number ends in an odd number, and when spelling them you always have to.. mention the final number.

these LLM's don't think too well.

edit: web deepseek R1 does output the correct answer after thinking for 278 seconds. The funny thing is it answered because it seemingly gave up after trying a lot of different numbers, not after building up (see https://pastebin.com/u2w9HuWC )

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After examining the spellings of odd numbers in English, it becomes evident that all odd numbers contain the letter 'e' in their written form. Here's the breakdown:

1. *1*: "one" (contains 'e') 2. *3*: "three" (contains 'e') 3. *5*: "five" (contains 'e') 4. *7*: "seven" (contains 'e') 5. *9*: "nine" (contains 'e') 6. All subsequent odd numbers (e.g., 11, 13, 15...) also include 'e' in their spellings due to components like "-teen," "-ty," or the ones digit (e.g., "one," "three," "five").

*Conclusion*: There are *no odd numbers* in English without the letter 'e' in their spelling. Therefore, the first three such numbers do not exist.