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I feel like powers of two would be quite a good alternative - "1", "2", "4", "8", "16".
No, as per @aggi that would give it unwarranted sense of scientific rigour, e.g that task A with 16 points is twice as big as task B with 8 points.
Also, conjecture: they are trivial to calculate, so don't need remembering, and intervals increase at a reasonable rate: faster than primes but slower than squares.
Gives it an unwaranted sense of scientific rigour probably. Like, you or I may not know why it's fibonacci numbers, but there's definitely a proper numerical reason why "1","2","3","4" wouldn't possibly work.
I feel like powers of two would be quite a good alternative - "1", "2", "4", "8", "16".