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A363164
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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.
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1
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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, 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, 2, 1, 1, 3, 3, 1, 1, 2, 1, 0, 0, 1, 2, 3, 4, 3, 6, 3, 4, 3, 2, 1, 0
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OFFSET
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0,13
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LINKS
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FORMULA
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A(n, k) = A(k, n).
A(n, 0) = 0.
A(n, 1) = 1 for any n > 0.
A(n, n) = n.
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EXAMPLE
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Table A(n, k) begins:
n\k | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
----+-----------------------------------------------------
0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 | 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 | 0 1 2 1 2 2 2 1 2 2 2 2 2 2 2 1
3 | 0 1 1 3 1 3 3 3 1 3 3 3 3 3 3 3
4 | 0 1 2 1 4 2 2 1 4 4 4 2 4 2 2 1
5 | 0 1 2 3 2 5 3 3 2 5 5 5 3 5 3 3
6 | 0 1 2 3 2 3 6 3 2 3 6 3 6 6 6 3
7 | 0 1 1 3 1 3 3 7 1 3 3 7 3 7 7 7
8 | 0 1 2 1 4 2 2 1 8 4 4 2 4 2 2 1
9 | 0 1 2 3 4 5 3 3 4 9 5 5 4 5 3 3
10 | 0 1 2 3 4 5 6 3 4 5 10 5 6 6 6 3
11 | 0 1 2 3 2 5 3 7 2 5 5 11 3 7 7 7
12 | 0 1 2 3 4 3 6 3 4 4 6 3 12 6 6 3
13 | 0 1 2 3 2 5 6 7 2 5 6 7 6 13 7 7
14 | 0 1 2 3 2 3 6 7 2 3 6 7 6 7 14 7
15 | 0 1 1 3 1 3 3 7 1 3 3 7 3 7 7 15
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PROG
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(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)); }
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CROSSREFS
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See A175466 for a similar sequence.
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KEYWORD
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AUTHOR
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STATUS
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approved
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