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

0,8

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.

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

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).

Example

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

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A014473 A226545 A343042 * A271917 A185651 A265080

Adjacent sequences: A343043 A343044 A343045 * A343047 A343048 A343049

Keyword

nonn,base,tabl

Author

Rémy Sigrist, Apr 05 2021

Status

approved