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 A380455 #52 Aug 04 2025 16:53:46 %S A380455 1,1,1,1,3,1,4,1,5,1,5,1 %N A380455 Maximum number of prime polyomino factors of an n-polyomino. %C A380455 Grade one students are capable of understanding "prime" and "composite" and "is a factor of" when presented in terms of polyomino tilings. Exploring these ideas is a 10/10 classroom activity, even if limited to only pentomino factors of larger polyominoes. %C A380455 Conjectured terms: a(14)..a(17) = 10?, 3, 12?, 1. %F A380455 a(p) = 1 if p is prime. - _Pontus von Brömssen_, Jun 24 2025 %e A380455 a(6) = 3 because the 2x3 rectangular hexomino can be tiled by three prime polyominoes: %e A380455 The domino: %e A380455 XOY %e A380455 XOY %e A380455 The bent tromino: %e A380455 XXO %e A380455 XOO %e A380455 The straight tromino: %e A380455 XXX %e A380455 OOO %e A380455 a(9) = 1 because no 9-polyomino can be tiled by both all straight and all bent trominoes. %e A380455 It is conjectured that a(14) = 10 because this 14-polyomino can be tiled with 9 prime heptominoes and by the domino: %e A380455 X %e A380455 XXXX %e A380455 XXXX %e A380455 XXXX %e A380455 X %e A380455 It is also conjectured that a(16) = 12 because this 16-polyomino can be tiled with twelve prime 8-polyominoes: %e A380455 XXX %e A380455 XXXXX %e A380455 XXXXX %e A380455 XXX %Y A380455 Cf. A342430 (number of prime polyominoes with n cells). %K A380455 nonn,more %O A380455 2,5 %A A380455 _Gordon Hamilton_, Jun 22 2025