A382028 Lexicographically earliest sequence of positive integers such that a(n) is the length of the n-th run of consecutive, equal terms and no two runs have the same product.
1, 2, 2, 3, 3, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, 4, 4, 4, 5, 5, 5, 6, 6, 6, 3, 3, 3, 3, 4, 4, 4, 4, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5
Offset: 1
Keywords
Examples
a(12)..a(13) = 4: This is the 6th run. a(6) = 2, so the 6th run has length 2. We cannot use 1 as any run of 1s would have the same product as the first run a(1) = 1. Runs of length 2 made of 2s and 3s have already occurred, so a(12)..a(13) = 4. a(27)..a(30) = 3: This is the 12th run. a(12) = 4, so the 12th run has length 4. We cannot use 1 for the same reason mentioned above. We cannot have 2 because a run of four 2s has product 16, which would be the same as that of the 6th run of two 4s. So a(27)..a(30) = 3, a run whose product has not occurred before in a previous run.
Links
- Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000