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%I #9 May 31 2021 02:11:35
%S 0,1,1,2,1,2,3,2,2,3,4,3,2,3,4,5,4,3,3,4,5,6,5,4,3,4,5,6,7,6,5,6,6,5,
%T 6,7,8,7,6,6,4,6,6,7,8,9,8,7,6,5,5,6,7,8,9,10,9,8,7,6,5,6,7,8,9,10,11,
%U 10,9,12,7,6,6,7,12,9,10,11,12,11,10,12,8,7,6,7,8,12,10,11,12
%N Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = max(n * 2^max(0, w(k)-w(n)), k * 2^max(0, w(n)-w(k))) (where w = A070939).
%C In other words, we right pad the binary expansion of the lesser of n and k with zeros (provided it is positive) so that both numbers have the same number of binary digits, and then take the greatest value.
%H Rémy Sigrist, <a href="/A344838/b344838.txt">Table of n, a(n) for n = 0..10010</a>
%H Rémy Sigrist, <a href="/A344838/a344838.png">Colored representation of the table for n, k < 2^10</a>
%F T(n, k) = T(k, n).
%F T(m, T(n, k)) = T(T(m, n), k).
%F T(n, n) = n.
%F T(n, 0) = n.
%F T(n, 1) = max(1, n).
%e Array T(n, k) begins:
%e n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
%e ---+----------------------------------------------------------------
%e 0| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
%e 1| 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
%e 2| 2 2 2 3 4 5 6 7 8 9 10 11 12 13 14 15
%e 3| 3 3 3 3 6 6 6 7 12 12 12 12 12 13 14 15
%e 4| 4 4 4 6 4 5 6 7 8 9 10 11 12 13 14 15
%e 5| 5 5 5 6 5 5 6 7 10 10 10 11 12 13 14 15
%e 6| 6 6 6 6 6 6 6 7 12 12 12 12 12 13 14 15
%e 7| 7 7 7 7 7 7 7 7 14 14 14 14 14 14 14 15
%e 8| 8 8 8 12 8 10 12 14 8 9 10 11 12 13 14 15
%e 9| 9 9 9 12 9 10 12 14 9 9 10 11 12 13 14 15
%e 10| 10 10 10 12 10 10 12 14 10 10 10 11 12 13 14 15
%e 11| 11 11 11 12 11 11 12 14 11 11 11 11 12 13 14 15
%e 12| 12 12 12 12 12 12 12 14 12 12 12 12 12 13 14 15
%e 13| 13 13 13 13 13 13 13 14 13 13 13 13 13 13 14 15
%e 14| 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 15
%e 15| 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15
%o (PARI) T(n,k,op=max,w=m->#binary(m)) = { op(n*2^max(0, w(k)-w(n)), k*2^max(0, w(n)-w(k))) }
%Y Cf. A003984, A070939.
%Y Cf. A344834 (AND), A344835 (OR), A344836 (XOR), A344837 (min), A344839 (absolute difference).
%K nonn,base,tabl
%O 0,4
%A _Rémy Sigrist_, May 29 2021