A363164 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.
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
Offset: 0
Examples
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
Links
- Rémy Sigrist, Colored representation of the array for n, k < 2^10
Programs
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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)); }
Formula
A(n, k) = A(k, n).
A(n, 0) = 0.
A(n, 1) = 1 for any n > 0.
A(n, n) = n.