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%I #11 Apr 08 2021 00:34:13
%S 0,1,1,2,1,2,3,3,3,3,4,3,2,3,4,5,5,3,3,5,5,6,5,4,3,4,5,6,7,7,5,5,5,5,
%T 7,7,8,7,8,5,4,5,8,7,8,9,9,9,9,5,5,9,9,9,9,10,9,8,9,10,5,10,9,8,9,10,
%U 11,11,9,9,11,11,11,11,9,9,11,11,12,11,10,9,10,11,6,11,10,9,10,11,12
%N Array T(n, k), n, k >= 0, read by antidiagonals; lunar addition table for the factorial base.
%C The i-th digit of T(n, k) in factorial base is the largest of the i-th digits of n and of k in factorial base.
%C For n = 0..23, the factorial and primorial base representations of n are the same; hence the date sections for this sequence and for A343044 are the same.
%H Rémy Sigrist, <a href="/A343040/b343040.txt">Table of n, a(n) for n = 0..10010</a>
%H Rémy Sigrist, <a href="/A343040/a343040.png">Colored representation of the array for n, k < 6!</a> (where the color is function of T(n, k))
%H <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F T(n, k) = T(k, n).
%F T(m, T(n, k)) = T(T(m, n), k).
%F T(n, 0) = n.
%F T(n, n) = n.
%e Array T(n, k) begins:
%e n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12
%e ---+----------------------------------------------------
%e 0| 0 1 2 3 4 5 6 7 8 9 10 11 12
%e 1| 1 1 3 3 5 5 7 7 9 9 11 11 13
%e 2| 2 3 2 3 4 5 8 9 8 9 10 11 14
%e 3| 3 3 3 3 5 5 9 9 9 9 11 11 15
%e 4| 4 5 4 5 4 5 10 11 10 11 10 11 16
%e 5| 5 5 5 5 5 5 11 11 11 11 11 11 17
%e 6| 6 7 8 9 10 11 6 7 8 9 10 11 12
%e 7| 7 7 9 9 11 11 7 7 9 9 11 11 13
%e 8| 8 9 8 9 10 11 8 9 8 9 10 11 14
%e 9| 9 9 9 9 11 11 9 9 9 9 11 11 15
%e 10| 10 11 10 11 10 11 10 11 10 11 10 11 16
%e 11| 11 11 11 11 11 11 11 11 11 11 11 11 17
%e 12| 12 13 14 15 16 17 12 13 14 15 16 17 12
%e Array T(n, k) begins in factorial base:
%e n\k| 0 1 10 11 20 21 100 101 110 111 120 121 200
%e ---+-----------------------------------------------------------------
%e 0| 0 1 10 11 20 21 100 101 110 111 120 121 200
%e 1| 1 1 11 11 21 21 101 101 111 111 121 121 201
%e 10| 10 11 10 11 20 21 110 111 110 111 120 121 210
%e 11| 11 11 11 11 21 21 111 111 111 111 121 121 211
%e 20| 20 21 20 21 20 21 120 121 120 121 120 121 220
%e 21| 21 21 21 21 21 21 121 121 121 121 121 121 221
%e 100| 100 101 110 111 120 121 100 101 110 111 120 121 200
%e 101| 101 101 111 111 121 121 101 101 111 111 121 121 201
%e 110| 110 111 110 111 120 121 110 111 110 111 120 121 210
%e 111| 111 111 111 111 121 121 111 111 111 111 121 121 211
%e 120| 120 121 120 121 120 121 120 121 120 121 120 121 220
%e 121| 121 121 121 121 121 121 121 121 121 121 121 121 221
%e 200| 200 201 210 211 220 221 200 201 210 211 220 221 200
%o (PARI) T(n,k) = { my (v=0, f=1); for (r=2, oo, if (n==0 && k==0, return (v), v+=max(n%r, k%r)*f; f*=r; n\=r; k\=r)) }
%Y Cf. A087061, A108731, A343040, A343044.
%K nonn,base,tabl
%O 0,4
%A _Rémy Sigrist_, Apr 03 2021