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 A375863 #60 Sep 02 2024 23:56:16 %S A375863 0,1,1,4,4,1,1,9,9,1,1,4,4,1,1,16,16,1,1,4,4,1,1,9,9,1,1,4,4,1,1,25, %T A375863 25,1,1,4,4,1,1,9,9,1,1,4,4,1,1,16,16,1,1,4,4,1,1,9,9,1,1,4,4,1,1,36, %U A375863 36,1,1,4,4,1,1,9,9,1,1,4,4,1,1,16,16,1,1,4,4,1,1,9,9,1,1,4,4,1,1,25 %N A375863 a(1) = 0 and a(n) = A050603(n-1)^2 for n > 0. Lexicographically earliest nonnegative sequence of integers such that the Gilbreath transform of a(1..n) gives floor(log_2(n)). %e A375863 The first row is the sequence itself. The rows below are the absolute differences %e A375863 of each previous row: %e A375863 0, 1, 1, 4, 4, 1, 1, 9, 9, 1, 1, 4, 4, 1, 1, 16, 16, ... %e A375863 1, 0, 3, 0, 3, 0, 8, 0, 8, 0, 3, 0, 3, 0, 15, 0, ... %e A375863 1, 3, 3, 3, 3, 8, 8, 8, 8, 3, 3, 3, 3, 15, 15, ... %e A375863 2, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 12, 0, ... %e A375863 2, 0, 0, 5, 5, 0, 0, 5, 5, 0, 0, 12, 12, ... %e A375863 2, 0, 5, 0, 5, 0, 5, 0, 5, 0, 12, 0, ... %e A375863 2, 5, 5, 5, 5, 5, 5, 5, 5, 12, 12, ... %e A375863 3, 0, 0, 0, 0, 0, 0, 0, 7, 0, ... %e A375863 3, 0, 0, 0, 0, 0, 0, 7, 7, ... %e A375863 3, 0, 0, 0, 0, 0, 7, 0, ... %e A375863 3, 0, 0, 0, 0, 7, 7, ... %e A375863 3, 0, 0, 0, 7, 0, ... %e A375863 3, 0, 0, 7, 7, ... %e A375863 3, 0, 7, 0, ... %e A375863 3, 7, 7, ... %e A375863 4, 0, ... %e A375863 4, ... %e A375863 The main diagonal is floor(log_2(n)), where n = 1 in the first row and n = 2 in the second etc. . %o A375863 (PARI) a(n) = if(n == 1, 0,valuation(n-(n-2)%2, 2)^2) %Y A375863 Cf. A050603, A039963 (Gilbreath transform of floor(log_2(n))). %K A375863 nonn %O A375863 1,4 %A A375863 _Thomas Scheuerle_, Sep 02 2024