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%I #23 Jul 13 2023 08:37:57
%S 0,0,0,0,1,0,0,1,1,0,0,1,2,1,0,0,1,1,1,1,0,0,1,2,3,2,1,0,0,1,2,1,1,2,
%T 1,0,0,1,2,3,4,3,2,1,0,0,1,1,3,2,2,3,1,1,0,0,1,2,3,2,5,2,3,2,1,0,0,1,
%U 2,1,1,3,3,1,1,2,1,0,0,1,2,3,4,3,6,3,4,3,2,1,0
%N Square array A(n, k), n, k >= 0, read by antidiagonals; A(n, k) is the greatest nonnegative number whose binary digits appear in order but not necessarily as consecutive digits in the binary expansions of n and k.
%H Rémy Sigrist, <a href="/A363164/a363164.png">Colored representation of the array for n, k < 2^10</a>
%F A(n, k) = A(k, n).
%F A(n, 0) = 0.
%F A(n, 1) = 1 for any n > 0.
%F A(n, n) = n.
%e Table A(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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e 1 | 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
%e 2 | 0 1 2 1 2 2 2 1 2 2 2 2 2 2 2 1
%e 3 | 0 1 1 3 1 3 3 3 1 3 3 3 3 3 3 3
%e 4 | 0 1 2 1 4 2 2 1 4 4 4 2 4 2 2 1
%e 5 | 0 1 2 3 2 5 3 3 2 5 5 5 3 5 3 3
%e 6 | 0 1 2 3 2 3 6 3 2 3 6 3 6 6 6 3
%e 7 | 0 1 1 3 1 3 3 7 1 3 3 7 3 7 7 7
%e 8 | 0 1 2 1 4 2 2 1 8 4 4 2 4 2 2 1
%e 9 | 0 1 2 3 4 5 3 3 4 9 5 5 4 5 3 3
%e 10 | 0 1 2 3 4 5 6 3 4 5 10 5 6 6 6 3
%e 11 | 0 1 2 3 2 5 3 7 2 5 5 11 3 7 7 7
%e 12 | 0 1 2 3 4 3 6 3 4 4 6 3 12 6 6 3
%e 13 | 0 1 2 3 2 5 6 7 2 5 6 7 6 13 7 7
%e 14 | 0 1 2 3 2 3 6 7 2 3 6 7 6 7 14 7
%e 15 | 0 1 1 3 1 3 3 7 1 3 3 7 3 7 7 15
%o (PARI) A(n, k) = { my (sn = [0], bn = binary(n), sk = [0], bk = binary(k)); for (i = 1, #bn, sn = setunion(sn, [2*v+bn[i]|v<-sn])); for (i = 1, #bk, sk = setunion(sk, [2*v+bk[i]|v<-sk])); vecmax(setintersect(sn, sk)); }
%Y See A175466 for a similar sequence.
%Y Cf. A301983.
%K nonn,base,tabl
%O 0,13
%A _Rémy Sigrist_, Jul 07 2023