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 A384034 #27 Jun 04 2025 10:24:47 %S A384034 1,1,2,1,3,2,4,5,1,6,3,7,8,9,2,10,11,4,12,13,14,15,5,16,17,18,19,20,1, %T A384034 21,6,22,23,24,25,26,27,3,28,29,30,7,31,32,33,34,35,36,37,8,38,39,40, %U A384034 41,42,43,44,45,9,46,47,48,49,50,51,52,53,54,2,55,56 %N A384034 Irregular triangle read by rows. Start with T(1,1) = 1. For each subsequent row, traverse the array so far. For each value m, insert m new values from the next unused integers immediately to the right of m. The process is repeated row by row, where each number in the array dictates how many new values are added after it. %e A384034 Triangle begins: %e A384034 1; %e A384034 1, 2; %e A384034 1, 3, 2, 4, 5; %e A384034 1, 6, 3, 7, 8, 9, 2, 10, 11, 4, 12, 13, 14, 15, 5, 16, 17, 18, 19, 20; %e A384034 ... %e A384034 Row 1 = [1]. %e A384034 For m = 1, insert 1 new integer (next unused is 2) to the right of 1. %e A384034 Row 2 = [1, 2]. %e A384034 For m = 1, insert 1 new integer (next unused is 3) to the right of 1. %e A384034 For m = 2, insert 2 new integers (next unused are 4, 5) to the right of 2. %e A384034 Row 3 = [1, 3, 2, 4, 5]. %e A384034 For m = 1, insert 1 new integer (6). %e A384034 For m = 3, insert 3 new integers (7, 8, 9). %e A384034 For m = 2, insert 2 new integers (10, 11). %e A384034 For m = 4, insert 4 new integers (12, 13, 14, 15). %e A384034 For m = 5, insert 5 new integers (16, 17, 18, 19, 20). %e A384034 Row 4 = [1, 6, 3, 7, 8, 9, 2, 10, 11, 4, 12, 13, 14, 15, 5, 16, 17, 18, 19, 20]. %e A384034 And so on. %K A384034 nonn,tabf %O A384034 1,3 %A A384034 _Ali Sada_, May 21 2025