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I think your obervation is due to palindromes in the differences between primes themselves. I worked through your example for the integers 8 to 16, the sequenc
by soVeryTired 8y ago
I think your obervation is due to palindromes in the differences between primes themselves.
I worked through your example for the integers 8 to 16, the sequence being 3 2 3 0 1 0 3 2 3.
The sequence of numbers we observe is due entirely to the locations of the primes 5, 7, 11, 13, 17, and 19.
The differences between these primes is 2, 4, 2, 4, 2, which is again a palindrome. I wouldn't be surprised if that's the reason your original sequence is palindromic. If it is, the question is then whether palindromes in distances between primes are unusually common.
- aerovistae 8y agoYou are correct! Great observation.
- soVeryTired 8y agoWeird, someone else pointed out the same thing on stackexchange around the same time I did. I guess they must have come from here.
- aerovistae 8y agoI was wondering if you were the same person with different account names on different sites! Evidently not.
- DavidSJ 8y agoI also came close to pointing that out, and then I noticed that it only makes palindromes of this sequence more probable, rather than guaranteeing them (see my comment on Math SE).