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 A343042 #15 Apr 08 2021 10:48:29 %S A343042 0,0,0,0,1,0,0,2,2,0,0,3,6,3,0,0,2,8,8,2,0,0,3,6,9,6,3,0,0,6,8,8,8,8, %T A343042 6,0,0,7,24,9,12,9,24,7,0,0,8,26,30,14,14,30,26,8,0,0,9,30,33,24,15, %U A343042 24,33,30,9,0,0,8,32,32,26,30,30,26,32,32,8,0 %N A343042 Array T(n, k), n, k >= 0, read by antidiagonals; lunar multiplication table for the factorial base. %C A343042 To compute T(n, k): %C A343042 - write the factorial base representations of n and of k on two lines, right aligned, %C A343042 - to "multiply" two digits: take the smallest, %C A343042 - to "add" two digits: take the largest, %C A343042 - for example, for T(13, 14): %C A343042 12 -> 2 0 1 %C A343042 14 -> x 2 1 0 %C A343042 ------- %C A343042 0 0 0 %C A343042 1 0 1 %C A343042 + 2 0 1 %C A343042 ----------- %C A343042 2 1 1 1 0 -> 272 = T(13, 14) %C A343042 See A343040 for the corresponding addition table. %H A343042 Rémy Sigrist, <a href="/A343042/b343042.txt">Table of n, a(n) for n = 0..10010</a> %H A343042 Rémy Sigrist, <a href="/A343042/a343042.gp.txt">PARI program for A343042</a> %H A343042 <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a> %H A343042 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a> %F A343042 T(n, k) = T(k, n). %F A343042 T(m, T(n, k)) = T(T(m, n), k). %F A343042 T(n, 0) = 0. %e A343042 Array T(n, k) begins: %e A343042 n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 %e A343042 ---+--------------------------------------------------------- %e A343042 0| 0 0 0 0 0 0 0 0 0 0 0 0 0 %e A343042 1| 0 1 2 3 2 3 6 7 8 9 8 9 6 %e A343042 2| 0 2 6 8 6 8 24 26 30 32 30 32 24 %e A343042 3| 0 3 8 9 8 9 30 33 32 33 32 33 30 %e A343042 4| 0 2 6 8 12 14 24 26 30 32 36 38 48 %e A343042 5| 0 3 8 9 14 15 30 33 32 33 38 39 54 %e A343042 6| 0 6 24 30 24 30 120 126 144 150 144 150 120 %e A343042 7| 0 7 26 33 26 33 126 127 152 153 152 153 126 %e A343042 8| 0 8 30 32 30 32 144 152 150 152 150 152 144 %e A343042 9| 0 9 32 33 32 33 150 153 152 153 152 153 150 %e A343042 10| 0 8 30 32 36 38 144 152 150 152 156 158 168 %e A343042 11| 0 9 32 33 38 39 150 153 152 153 158 159 174 %e A343042 12| 0 6 24 30 48 54 120 126 144 150 168 174 240 %o A343042 (PARI) See Links section. %Y A343042 Cf. A087062, A343040, A343046. %K A343042 nonn,base,tabl %O A343042 0,8 %A A343042 _Rémy Sigrist_, Apr 05 2021