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A355246
Square array A(n, k), n, k >= 0, read by antidiagonals; for any m > 0, the position of the m-th rightmost 0 in the binary expansion of A(n, k) is the greatest of the positions of the m-th rightmost 0 in the binary expansions of n and k (the least significant bit having position 0).
1
0, 1, 1, 2, 1, 2, 3, 1, 1, 3, 4, 3, 2, 3, 4, 5, 1, 3, 3, 1, 5, 6, 5, 2, 3, 2, 5, 6, 7, 5, 5, 3, 3, 5, 5, 7, 8, 7, 6, 3, 4, 3, 6, 7, 8, 9, 1, 7, 3, 5, 5, 3, 7, 1, 9, 10, 9, 2, 7, 6, 5, 6, 7, 2, 9, 10, 11, 9, 9, 3, 7, 5, 5, 7, 3, 9, 9, 11, 12, 11, 10, 3, 4, 7, 6, 7, 4, 3, 10, 11, 12
OFFSET
0,4
COMMENTS
Leading 0's are taken into account.
FORMULA
A(n, k) = A(k, n).
A(m, A(n, k)) = A(A(m, n), k).
A(n, n) = n.
A(n, n) = 0.
A(n, k) < 2^m for any n < 2^m and k < 2^m.
A(m, A355245(n, k)) = A355245(A(m, n), A(m, k)).
A355245(m, A(n, k)) = A(A355245(m, n), A355245(m, k)).
EXAMPLE
Array A(n, k) begins:
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
---+----------------------------------------------------------
0| 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1| 1 1 1 3 1 5 5 7 1 9 9 11 9 13 13 15
2| 2 1 2 3 2 5 6 7 2 9 10 11 10 13 14 15
3| 3 3 3 3 3 3 3 7 3 3 3 11 3 11 11 15
4| 4 1 2 3 4 5 6 7 4 9 10 11 12 13 14 15
5| 5 5 5 3 5 5 5 7 5 5 5 11 5 13 13 15
6| 6 5 6 3 6 5 6 7 6 5 6 11 6 13 14 15
7| 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 15
8| 8 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
9| 9 9 9 3 9 5 5 7 9 9 9 11 9 13 13 15
10| 10 9 10 3 10 5 6 7 10 9 10 11 10 13 14 15
.
For n = 876 and k = 425:
- the corresponding binary expansions and pairings of 0's are as follows (stars indicate greatest positions of 0's):
* * * * *
876 ... 0 0 0 1 1 0 1 1 0 1 1 0 0
\ \ \ \ | / /
425 ... 0 0 0 0 1 1 0 1 0 1 0 0 1
* * *
-----------------------------
873 ... 0 0 0 1 1 0 1 1 0 1 0 0 1
- so A(876, 425) = 873.
PROG
(PARI) A(n, k) = { my (v=0, zn=0, zk=0, w=1, b=1); while (n || k, if (n%2==0, zn++); if (k%2==0, zk++); if (min(zn, zk)==w, w++, v+=b); n\=2; k\=2; b*=2); v }
CROSSREFS
See A355245 for a similar sequence.
Sequence in context: A159335 A109004 A103823 * A136642 A080382 A349203
KEYWORD
nonn,base,tabl
AUTHOR
Rémy Sigrist, Jun 25 2022
STATUS
approved