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A342955
Array T(n,k), n, k >= 0, read by antidiagonals; the i-th decimal digit of T(n, k) is the smallest of the i-th digits of n and of k.
1
0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 0, 0, 2, 3, 4, 5, 5, 4, 3, 2, 0, 0, 0, 1, 0, 3, 4, 5, 6, 5, 4, 3, 0, 1, 0
OFFSET
0,13
COMMENTS
This sequence has similarities with lunar addition (A087061); here we take the smallest, there the largest digits. It is "lunar multiplication" of corresponding digits.
The bitwise AND operator (A004198) is the binary analog.
LINKS
Rémy Sigrist, Colored representation of the array for n, k < 1000 (where the color is function of T(n, k))
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, k) + A087061(n, k) = n + k.
EXAMPLE
Array T(n, k) begins:
n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13
---+----------------------------------------------
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 0 1 1 1
2| 0 1 2 2 2 2 2 2 2 2 0 1 2 2
3| 0 1 2 3 3 3 3 3 3 3 0 1 2 3
4| 0 1 2 3 4 4 4 4 4 4 0 1 2 3
5| 0 1 2 3 4 5 5 5 5 5 0 1 2 3
6| 0 1 2 3 4 5 6 6 6 6 0 1 2 3
7| 0 1 2 3 4 5 6 7 7 7 0 1 2 3
8| 0 1 2 3 4 5 6 7 8 8 0 1 2 3
9| 0 1 2 3 4 5 6 7 8 9 0 1 2 3
10| 0 0 0 0 0 0 0 0 0 0 10 10 10 10
11| 0 1 1 1 1 1 1 1 1 1 10 11 11 11
12| 0 1 2 2 2 2 2 2 2 2 10 11 12 12
13| 0 1 2 3 3 3 3 3 3 3 10 11 12 13
PROG
(PARI) T(n, k, base=10) = if (n==0 || k==0, 0, T(n\base, k\base)*base + min(n%base, k%base))
CROSSREFS
Cf. A004197 (numerical minimum), A004198 (bitwise minimum), A087061 (digit-wise maximum).
Sequence in context: A359902 A111143 A356969 * A004197 A261684 A048571
KEYWORD
nonn,tabl,base,easy,look
AUTHOR
Rémy Sigrist, Apr 03 2021
STATUS
approved