x.com/Math_files/status/2113978495319822762
1 correction found
It records the smallest positive multiple of each integer whose digits alternate in parity, using a special convention for multiples of 20.
OEIS A343335 is defined as the smallest proper alternating multiple of n, not simply the smallest positive alternating multiple. In particular, the entry excludes n itself when n already has alternating-parity digits.
Full reasoning
The OEIS definition for A343335 is more specific than the post states. OEIS says:
- "a(n) is the smallest proper alternating multiple of n when n is not a multiple of 20".
- It further explains: "a(n) is the smallest alternating multiple k*n, with k > 1".
That means the sequence does not record the smallest positive alternating multiple in general, because it excludes the trivial case where the multiple is just n itself. For example, the sequence begins 2, 4, 6, 8, 10, ..., so for n = 1 it gives a(1) = 2, not 1; for n = 2 it gives a(2) = 4, not 2. The post's wording omits the crucial word "proper", which changes the mathematical definition.
The part about multiples of 20 being handled specially is correct: OEIS sets a(20k)=0 because such numbers have no alternating multiple. But the overall sentence is still inaccurate because it misstates what the sequence records.
1 source
- OEIS A343335
a(n) is the smallest proper alternating multiple of n when n is not a multiple of 20, otherwise a(20*k) = 0 for k >= 1. ... If n is an alternator, n <> 20*k, k>=1, then a(n) is the smallest alternating multiple k*n, with k > 1.