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 A323420 #22 Aug 31 2019 03:09:44 %S A323420 1,2,1,3,1,2,4,3,1,2,5,3,1,2,4,6,1,2,5,3,1,7,4,6,1,2,5,3,8,7,4,6,1,2, %T A323420 5,3,9,7,4,6,1,2,5,3,8,10,4,6,1,2,5,3,9,7,4,11,1,2,5,3,8,10,4,6,1,2, %U A323420 12,3,9,7,4,11,1,2,5,3,8,10,13,6,1,2,12,3 %N A323420 Lexicographically earliest sequence of positive integers such that for any n > 0, a(n + a(n)) > a(n). %C A323420 Every positive integer appears in the sequence. %C A323420 Empirically: %C A323420 - for any n > 0, the least d > 0 such that a(n) = a(n+d) is a power of 2 (see scatterplot in Links section), %C A323420 - the run-length transform of the first differences of the positions of the 1's in the sequence corresponds to A055010 (excluding the leading 0). %H A323420 Rémy Sigrist, <a href="/A323420/b323420.txt">Table of n, a(n) for n = 1..10000</a> %H A323420 Rémy Sigrist, <a href="/A323420/a323420.png">Colored scatterplot of the first 100000 terms</a> (where the color is function of the least d > 0 such that a(n) = a(n+d)) %F A323420 a(A000124(n)) = n + 1 for any n >= 0. %e A323420 a(1) = 1, hence a(1 + a(1)) = a(2) > 1. %e A323420 a(2) = 2, hence a(2 + a(2)) = a(4) > 2. %e A323420 a(3) = 1, hence a(3 + a(1)) = a(4) > 1. %e A323420 a(4) = 3, etc. %o A323420 (PARI) a = vector(84, n, 1); for (n=1, #a, print1 (a[n] ", "); nan = n+a[n]; if (nan <= #a, a[nan] = max(a[nan], 1+a[n]))) %Y A323420 Cf. A000124, A055010. %K A323420 nonn %O A323420 1,2 %A A323420 _Rémy Sigrist_, Aug 30 2019