|
%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
|
