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A051776 Table T(n,m) = Nim-product of n and m, read by antidiagonals, for n >= 1, m >= 1.

%I A051776 #22 Dec 20 2016 21:00:20
%S A051776 1,2,2,3,3,3,4,1,1,4,5,8,2,8,5,6,10,12,12,10,6,7,11,15,6,15,11,7,8,9,
%T A051776 13,2,2,13,9,8,9,12,14,14,7,14,14,12,9,10,14,4,10,8,8,10,4,14,10,11,
%U A051776 15,7,11,13,5,13,11,7,15,11,12,13,5,15,3,3,3,3,15,5
%N A051776 Table T(n,m) = Nim-product of n and m, read by antidiagonals, for n >= 1, m >= 1.
%D A051776 J. H. Conway, On Numbers and Games, Academic Press, p. 52.
%H A051776 R. J. Mathar, <a href="/A051776/b051776.txt">Table of n, a(n) for n = 1..1830</a>
%H A051776 H. W. Lenstra, <a href="http://hdl.handle.net/1887/2125">Nim multiplication</a>, (1978)
%H A051776 <a href="/index/Ni#Nimmult">Index entries for sequences related to Nim-multiplication</a>
%F A051776 T(n,m) = A051775(n,m).
%e A051776 Table begins:
%e A051776   1  2  3  4  5  6 ...
%e A051776   2  3  1  8 10 11 ...
%e A051776   3  1  2 12 15 13 ...
%e A051776   4  8 12  6  2 14 ...
%p A051776 We continue from A003987: to compute a Nim-multiplication table using (a) an addition table AT := array(0..NA, 0..NA) and (b) a nimsum procedure for larger values; MT := array(0..N,0..N); for a from 0 to N do MT[a,0] := 0; MT[0,a] := 0; MT[a,1] := a; MT[1,a] := a; od: for a from 2 to N do for b from a to N do t1 := {}; for i from 0 to a-1 do for j from 0 to b-1 do u1 := MT[i,b]; u2 := MT[a,j];
%p A051776 if u1<=NA and u2<=NA then u12 := AT[u1,u2]; else u12 := nimsum(u1,u2); fi; u3 := MT[i,j]; if u12<=NA and u3<=NA then u4 := AT[u12,u3]; else u4 := nimsum(u12,u3); fi; t1 := { op(t1), u4}; #t1 := { op(t1), AT[ AT[ MT[i,b], MT[a,j] ], MT[i,j] ] }; od; od;
%p A051776 t2 := sort(convert(t1,list)); j := nops(t2); for i from 1 to nops(t2) do if t2[i] <> i-1 then j := i-1; break; fi; od; MT[a,b] := j; MT[b,a] := j; od; od;
%Y A051776 Cf. A051775, A003987, A051910.
%K A051776 tabl,nonn,easy,nice
%O A051776 1,2
%A A051776 _N. J. A. Sloane_, Dec 19 1999