A343046 - OEIS

%I #13 Apr 08 2021 10:49:22

%S 0,0,0,0,1,0,0,2,2,0,0,3,6,3,0,0,2,8,8,2,0,0,3,6,9,6,3,0,0,6,8,8,8,8,

%T 6,0,0,7,30,9,12,9,30,7,0,0,8,32,36,14,14,36,32,8,0,0,9,36,39,30,15,

%U 30,39,36,9,0,0,8,38,38,32,36,36,32,38,38,8,0

%N Array T(n, k), n, k >= 0, read by antidiagonals; lunar multiplication table for the primorial base.

%C To compute T(n, k):

%C - write the primorial base representations of n and of k on two lines, right aligned,

%C - to "multiply" two digits: take the smallest,

%C - to "add" two digits: take the largest,

%C - for example, for T(9, 10):

%C       9   ->   1 1 1

%C      10   -> x 1 2 0

%C              -------

%C                0 0 0

%C              1 1 1

%C          + 1 1 1

%C          -----------

%C            1 1 1 1 0  ->  248 = T(9, 10)

%C See A343044 for the corresponding addition table.

%H Rémy Sigrist, <a href="/A343046/b343046.txt">Table of n, a(n) for n = 0..10010</a>

%H Rémy Sigrist, <a href="/A343046/a343046.gp.txt">PARI program for A343046</a>

%H <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

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

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

%F T(n, 0) = 0.

%F T(n, 1) = A328841(n).

%F T(n, n) = A343047(n).

%e Array T(n, k) begins:

%e   n\k|  0  1   2   3   4   5    6    7    8    9   10   11   12

%e   ---+---------------------------------------------------------

%e     0|  0  0   0   0   0   0    0    0    0    0    0    0    0

%e     1|  0  1   2   3   2   3    6    7    8    9    8    9    6  ->  A328841

%e     2|  0  2   6   8   6   8   30   32   36   38   36   38   30

%e     3|  0  3   8   9   8   9   36   39   38   39   38   39   36

%e     4|  0  2   6   8  12  14   30   32   36   38   42   44   60

%e     5|  0  3   8   9  14  15   36   39   38   39   44   45   66

%e     6|  0  6  30  36  30  36  210  216  240  246  240  246  210

%e     7|  0  7  32  39  32  39  216  217  248  249  248  249  216

%e     8|  0  8  36  38  36  38  240  248  246  248  246  248  240

%e     9|  0  9  38  39  38  39  246  249  248  249  248  249  246

%e    10|  0  8  36  38  42  44  240  248  246  248  252  254  270

%e    11|  0  9  38  39  44  45  246  249  248  249  254  255  276

%e    12|  0  6  30  36  60  66  210  216  240  246  270  276  420

%o (PARI) See Links section.

%Y Cf. A087062, A235168, A328841, A343042, A343044, A343047.

%K nonn,base,tabl

%O 0,8

%A _Rémy Sigrist_, Apr 05 2021