cp's OEIS Frontend

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.

%I A342955 #62 Aug 18 2022 22:45:38
%S A342955 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,
%T A342955 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,
%U A342955 2,3,4,5,5,4,3,2,0,0,0,1,0,3,4,5,6,5,4,3,0,1,0
%N 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.
%C A342955 This sequence has similarities with lunar addition (A087061); here we take the smallest, there the largest digits.  It is "lunar multiplication" of corresponding digits.
%C A342955 The bitwise AND operator (A004198) is the binary analog.
%H A342955 Rémy Sigrist, <a href="/A342955/b342955.txt">Table of n, a(n) for n = 0..10010</a>
%H A342955 Rémy Sigrist, <a href="/A342955/a342955.png">Colored representation of the array for n, k < 1000</a> (where the color is function of T(n, k))
%F A342955 T(n, k) = T(k, n).
%F A342955 T(m, T(n, k)) = T(T(m, n), k).
%F A342955 T(n, n) = n.
%F A342955 T(n, 0) = 0.
%F A342955 T(n, k) + A087061(n, k) = n + k.
%e A342955 Array T(n, k) begins:
%e A342955   n\k|  0  1  2  3  4  5  6  7  8  9  10  11  12  13
%e A342955   ---+----------------------------------------------
%e A342955     0|  0  0  0  0  0  0  0  0  0  0   0   0   0   0
%e A342955     1|  0  1  1  1  1  1  1  1  1  1   0   1   1   1
%e A342955     2|  0  1  2  2  2  2  2  2  2  2   0   1   2   2
%e A342955     3|  0  1  2  3  3  3  3  3  3  3   0   1   2   3
%e A342955     4|  0  1  2  3  4  4  4  4  4  4   0   1   2   3
%e A342955     5|  0  1  2  3  4  5  5  5  5  5   0   1   2   3
%e A342955     6|  0  1  2  3  4  5  6  6  6  6   0   1   2   3
%e A342955     7|  0  1  2  3  4  5  6  7  7  7   0   1   2   3
%e A342955     8|  0  1  2  3  4  5  6  7  8  8   0   1   2   3
%e A342955     9|  0  1  2  3  4  5  6  7  8  9   0   1   2   3
%e A342955    10|  0  0  0  0  0  0  0  0  0  0  10  10  10  10
%e A342955    11|  0  1  1  1  1  1  1  1  1  1  10  11  11  11
%e A342955    12|  0  1  2  2  2  2  2  2  2  2  10  11  12  12
%e A342955    13|  0  1  2  3  3  3  3  3  3  3  10  11  12  13
%o A342955 (PARI) T(n,k,base=10) = if (n==0 || k==0, 0, T(n\base,k\base)*base + min(n%base, k%base))
%Y A342955 Cf. A004197 (numerical minimum), A004198 (bitwise minimum), A087061 (digit-wise maximum).
%K A342955 nonn,tabl,base,easy,look
%O A342955 0,13
%A A342955 _Rémy Sigrist_, Apr 03 2021