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A325821 Multiplication table for carryless product i X j in base 3 for i >= 1 and j >= 1, read by antidiagonals.

%I A325821 #12 May 28 2019 19:35:29
%S A325821 1,2,2,3,1,3,4,6,6,4,5,8,9,8,5,6,7,12,12,7,6,7,3,15,16,15,3,7,8,5,18,
%T A325821 11,11,18,5,8,9,4,21,24,13,24,21,4,9,10,18,24,19,21,21,19,24,18,10,11,
%U A325821 20,27,23,26,9,26,23,27,20,11,12,19,30,36,19,15,15,19,36,30,19,12,13,24,33,40,45,12,13,12,45,40,33,24,13,14,26,36,44,50,54,11,11,54,50,44,36,26,14
%N A325821 Multiplication table for carryless product i X j in base 3 for i >= 1 and j >= 1, read by antidiagonals.
%C A325821 This is table A325820 without the zero row and column. See there for more comments.
%H A325821 Antti Karttunen, <a href="/A325821/b325821.txt">Table of n, a(n) for n = 1..5050; the first 100 antidiagonals of array</a>
%H A325821 <a href="/index/Ca#CARRYLESS">Index entries for sequences related to carryless arithmetic</a>
%e A325821 The array begins as:
%e A325821    1,  2,  3,  4,  5,  6,  7,  8,   9,  10,  11,  12, ...
%e A325821    2,  1,  6,  8,  7,  3,  5,  4,  18,  20,  19,  24, ...
%e A325821    3,  6,  9, 12, 15, 18, 21, 24,  27,  30,  33,  36, ...
%e A325821    4,  8, 12, 16, 11, 24, 19, 23,  36,  40,  44,  48, ...
%e A325821    5,  7, 15, 11, 13, 21, 26, 19,  45,  50,  52,  33, ...
%e A325821    6,  3, 18, 24, 21,  9, 15, 12,  54,  60,  57,  72, ...
%e A325821    7,  5, 21, 19, 26, 15, 13, 11,  63,  70,  68,  57, ...
%e A325821    8,  4, 24, 23, 19, 12, 11, 16,  72,  80,  76,  69, ...
%e A325821    9, 18, 27, 36, 45, 54, 63, 72,  81,  90,  99, 108, ...
%e A325821   10, 20, 30, 40, 50, 60, 70, 80,  90, 100,  83, 120, ...
%e A325821   11, 19, 33, 44, 52, 57, 68, 76,  99,  83,  91, 132, ...
%e A325821   12, 24, 36, 48, 33, 72, 57, 69, 108, 120, 132, 144, ...
%o A325821 (PARI)
%o A325821 up_to = 105;
%o A325821 A325820sq(b, c) = fromdigits(Vec(Pol(digits(b,3))*Pol(digits(c,3)))%3, 3);
%o A325821 A325821list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A325820sq(col,(a-(col-1))))); (v); };
%o A325821 v325821 = A325821list(up_to);
%o A325821 A325821(n) = v325821[n];
%Y A325821 Cf. A003991, A091257, A325820.
%K A325821 nonn,base,tabl
%O A325821 1,2
%A A325821 _Antti Karttunen_, May 22 2019