3 ms·
Is there a sequence where the sequence and all its differences contain each positive integer once? Something like 1 3 9 26 66 2 6 17 40 4
by OscarCunningham 1y ago
Is there a sequence where the sequence and all its differences contain each positive integer once?
Something like
1 3 9 26 66
2 6 17 40
4 11 23
7 12
5
Oh, here it is: https://oeis.org/A035313 https://oeis.org/A035313
- deleted 1y ago[deleted]
- thaumasiotes 1y ago> Oh, here it is: https://oeis.org/A035313 https://oeis.org/A035313 That sequence is not known to match what you asked for: >> Conjecturally, every positive integer occurs in the sequence or one of its n-th differences, which would imply that the sequence and its n-th differences partition the positive integers. For an intuition of why this might be hard to prove, note that you had to insert 7 into your structure before you inserted 5. In the general case, there might be a long waiting period before you're able to place some particular integer n. It might be infinitely long.