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Consecutive numbers, by definition, don't differ by 17. It would have to be something like consecutive square numbers (64 and 81).
The square root of 300 is irrational. Irrational numbers are infinitely dense and therefore the concept of consecutive numbers cannot be applied to irrational numbers.
There are no three consecutive numbers that are squares. Otherwise, there are an infinite sets of squares of three consecutive numbers: for example, {1,4,9}, or {4,9,16} or {576, 625, 676}
16,17,18,19,20,21,22,23,24,25.
The square roots of 338 are approx -18 and +18. So 0 and 1 are consecutive numbers that are between them.