A343046 Array T(n, k), n, k >= 0, read by antidiagonals; lunar multiplication table for the primorial base.

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

Offset: 0

Author

Rémy Sigrist, Apr 05 2021

Keywords

• nonn
• base
• tabl

Comments

To compute T(n, k):

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

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

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

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

9 -> 1 1 1

10 -> x 1 2 0

-------

0 0 0

1 1 1

+ 1 1 1

-----------

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

See A343044 for the corresponding addition table.

Examples

			Array T(n, k) begins:
  n\k|  0  1   2   3   4   5    6    7    8    9   10   11   12
  ---+---------------------------------------------------------
    0|  0  0   0   0   0   0    0    0    0    0    0    0    0
    1|  0  1   2   3   2   3    6    7    8    9    8    9    6  ->  A328841
    2|  0  2   6   8   6   8   30   32   36   38   36   38   30
    3|  0  3   8   9   8   9   36   39   38   39   38   39   36
    4|  0  2   6   8  12  14   30   32   36   38   42   44   60
    5|  0  3   8   9  14  15   36   39   38   39   44   45   66
    6|  0  6  30  36  30  36  210  216  240  246  240  246  210
    7|  0  7  32  39  32  39  216  217  248  249  248  249  216
    8|  0  8  36  38  36  38  240  248  246  248  246  248  240
    9|  0  9  38  39  38  39  246  249  248  249  248  249  246
   10|  0  8  36  38  42  44  240  248  246  248  252  254  270
   11|  0  9  38  39  44  45  246  249  248  249  254  255  276
   12|  0  6  30  36  60  66  210  216  240  246  270  276  420
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10010
• Rémy Sigrist, PARI program for A343046
• Index entries for sequences related to dismal (or lunar) arithmetic
• Index entries for sequences related to primorial base

Crossrefs

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

Programs

PARI

See Links section.

Formula

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

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

T(n, 0) = 0.

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

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