A344837 - OEIS

A344837

Square array T(n, k), n, k >= 0, read by antidiagonals; T(n, k) = min(n * 2^max(0, w(k)-w(n)), k * 2^max(0, w(n)-w(k))) (where w = A070939).

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 4, 2, 2, 4, 0, 0, 4, 4, 3, 4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 4, 4, 5, 4, 5, 4, 4, 0, 0, 8, 4, 6, 4, 4, 6, 4, 8, 0, 0, 8, 8, 6, 4, 5, 4, 6, 8, 8, 0, 0, 8, 8, 8, 4, 5, 5, 4, 8, 8, 8, 0, 0, 8, 8, 9, 8, 5, 6, 5, 8, 9, 8, 8, 0

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OFFSET

0,8

COMMENTS

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 least value.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..10010

Rémy Sigrist, Colored representation of the table for n, k < 2^10

FORMULA

T(n, k) = T(k, n).

T(m, T(n, k)) = T(T(m, n), k).

T(n, n) = n.

T(n, 0) = 0.

T(n, 1) = A053644(n).

EXAMPLE

Array T(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 2 2 4 4 4 4 8 8 8 8 8 8 8 8

2| 0 2 2 2 4 4 4 4 8 8 8 8 8 8 8 8

3| 0 2 2 3 4 5 6 6 8 9 10 11 12 12 12 12

4| 0 4 4 4 4 4 4 4 8 8 8 8 8 8 8 8

5| 0 4 4 5 4 5 5 5 8 9 10 10 10 10 10 10

6| 0 4 4 6 4 5 6 6 8 9 10 11 12 12 12 12

7| 0 4 4 6 4 5 6 7 8 9 10 11 12 13 14 14

8| 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

9| 0 8 8 9 8 9 9 9 8 9 9 9 9 9 9 9

10| 0 8 8 10 8 10 10 10 8 9 10 10 10 10 10 10

11| 0 8 8 11 8 10 11 11 8 9 10 11 11 11 11 11

12| 0 8 8 12 8 10 12 12 8 9 10 11 12 12 12 12

13| 0 8 8 12 8 10 12 13 8 9 10 11 12 13 13 13

14| 0 8 8 12 8 10 12 14 8 9 10 11 12 13 14 14

15| 0 8 8 12 8 10 12 14 8 9 10 11 12 13 14 15

PROG

(PARI) T(n, k, op=min, w=m->#binary(m)) = { op(n*2^max(0, w(k)-w(n)), k*2^max(0, w(n)-w(k))) }

CROSSREFS

Cf. A003983, A053644, A070939.

Cf. A344834 (AND), A344835 (OR), A344836 (XOR), A344838 (max), A344839 (absolute difference).

Sequence in context: A225869 A039972 A344834 * A031124 A063695 A081417

Adjacent sequences: A344834 A344835 A344836 * A344838 A344839 A344840

KEYWORD

nonn,base,tabl

AUTHOR

Rémy Sigrist, May 29 2021

STATUS

approved