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 A274821 #42 Sep 13 2020 01:59:12 %S A274821 1,2,3,2,3,2,3,1,4,1,5,4,6,4,5,6,4,5,7,6,7,8,5,7,6,8,7,4,1,7,6,8,1,7, %T A274821 8,6,5,9,2,4,7,9,2,10,8,9,3,5,10,9,3,11,12,9,10,11,13,4,9,10,8,11,10, %U A274821 3,5,9,6,11,3,12,10,12,1,11,8,9,7,1,10,8,11,13,8,2,5,9,6,12,2,11,13,10,6,12,11,14,13,12,14,15 %N A274821 Hexagonal spiral constructed on the nodes of the infinite triangular net in which each term is the least positive integer such that no diagonal contains a repeated term. %C A274821 Also spiral constructed on the infinite hexagonal grid in which each term is the least positive integer such that no diagonal of successive adjacent cells contains a repeated term. Every number is located in the center of a hexagonal cell. Every cell is also the center of three diagonals of successive adjacent cells. %F A274821 a(n) = A274820(n) + 1. %e A274821 Illustration of initial terms as a spiral: %e A274821 . %e A274821 . 10 - 5 - 3 - 9 - 8 %e A274821 . / \ %e A274821 . 9 4 - 7 - 8 - 6 10 %e A274821 . / / \ \ %e A274821 . 3 1 6 - 4 - 5 7 2 %e A274821 . / / / \ \ \ %e A274821 . 11 7 4 2 - 3 1 5 9 %e A274821 . / / / / \ \ \ \ %e A274821 . 12 6 5 3 1 - 2 4 8 7 %e A274821 . \ \ \ \ / / / %e A274821 . 9 8 6 2 - 3 - 1 7 4 %e A274821 . \ \ \ / / %e A274821 . 10 1 4 - 5 - 7 - 6 2 %e A274821 . \ \ / %e A274821 . 11 7 - 8 - 6 - 5 - 9 %e A274821 . \ %e A274821 . 13 - 4 - 9 - 10 - 8 %e A274821 . %Y A274821 Cf. A269526 (square array), A274640 (square spiral), A274651 (right triangle), A274820, A274920, A274921, A275606, A275610. %K A274821 nonn %O A274821 0,2 %A A274821 _Omar E. Pol_, Jul 09 2016