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 A354438 #15 Jan 05 2024 12:29:34
%S A354438 0,1,1,2,0,2,3,3,3,3,4,2,4,2,4,5,5,5,5,5,5,6,4,0,4,0,4,6,7,7,1,1,1,1,
%T A354438 7,7,8,6,8,0,2,0,8,6,8,9,9,9,9,3,3,9,9,9,9,10,8,10,8,10,2,10,8,10,8,
%U A354438 10,11,11,11,11,11,11,11,11,11,11,11,11
%N A354438 Square array A(n, k), n, k >= 0, read by antidiagonals; the factorial base expansion of A(n, k) is obtained by adding componentwise and reducing modulo their radix the digits of the factorial base expansions of n and k.
%C A354438 The nonnegative integers together with A form an abelian group; A225901 gives inverse elements.
%C A354438 Each row is a permutation of the nonnegative integers.
%H A354438 Andrew Howroyd, <a href="/A354438/b354438.txt">Table of n, a(n) for n = 0..1325</a> (first 51 antidiagonals)
%H A354438 Rémy Sigrist, <a href="/A354438/a354438.png">Colored representation of the array A(n, k) for n, k < 7!</a> (the hue is function of A(n, k), black pixels correspond to 0's)
%H A354438 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A354438 A(n, k) = A(k, n).
%F A354438 A(m, A(n, k)) = A(A(m, n), k).
%F A354438 A(n, 0) = n.
%F A354438 A(n, k) = 0 iff k = A225901(n).
%F A354438 A(n, 1) = A004442(n).
%e A354438 Square array A(n, k) begins:
%e A354438 n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
%e A354438 ---+----------------------------------------------------------------
%e A354438 0| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
%e A354438 1| 1 0 3 2 5 4 7 6 9 8 11 10 13 12 15 14
%e A354438 2| 2 3 4 5 0 1 8 9 10 11 6 7 14 15 16 17
%e A354438 3| 3 2 5 4 1 0 9 8 11 10 7 6 15 14 17 16
%e A354438 4| 4 5 0 1 2 3 10 11 6 7 8 9 16 17 12 13
%e A354438 5| 5 4 1 0 3 2 11 10 7 6 9 8 17 16 13 12
%e A354438 6| 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
%e A354438 7| 7 6 9 8 11 10 13 12 15 14 17 16 19 18 21 20
%e A354438 8| 8 9 10 11 6 7 14 15 16 17 12 13 20 21 22 23
%e A354438 9| 9 8 11 10 7 6 15 14 17 16 13 12 21 20 23 22
%e A354438 10| 10 11 6 7 8 9 16 17 12 13 14 15 22 23 18 19
%e A354438 11| 11 10 7 6 9 8 17 16 13 12 15 14 23 22 19 18
%e A354438 12| 12 13 14 15 16 17 18 19 20 21 22 23 0 1 2 3
%e A354438 13| 13 12 15 14 17 16 19 18 21 20 23 22 1 0 3 2
%e A354438 14| 14 15 16 17 12 13 20 21 22 23 18 19 2 3 4 5
%e A354438 15| 15 14 17 16 13 12 21 20 23 22 19 18 3 2 5 4
%o A354438 (PARI) A(n,k, s=i->i+1) = { my (v=0, f=1, r); for (i=1, oo, if (n==0 && k==0, return (v), r=s(i); v+=f*((n+k)%r); f*=r; n\=r; k\=r)) }
%Y A354438 Cf. A003987, A004442, A108731, A225901, A354470 (primorial base analog).
%K A354438 nonn,tabl,base
%O A354438 0,4
%A A354438 _Rémy Sigrist_, May 28 2022