This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382028 #15 Mar 29 2025 10:45:50 %S A382028 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, %T A382028 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, %U A382028 4,4,4,4,4,5,5,5,5,5,6,6,6,6,6,5,5,5,5,5,5 %N 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. %H A382028 Neal Gersh Tolunsky, <a href="/A382028/b382028.txt">Table of n, a(n) for n = 1..10000</a> %e A382028 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. %e A382028 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. %Y A382028 Cf. A331910, A381894, A000002. %K A382028 nonn %O A382028 1,2 %A A382028 _Neal Gersh Tolunsky_, Mar 12 2025