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

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, 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, 15, 7, 11, 13, 5, 13, 11, 7, 15, 11, 12, 13, 5, 15, 3, 3, 3, 3, 15, 5

Offset: 1

Author

N. J. A. Sloane, Dec 19 1999

Keywords

• tabl
• nonn
• easy
• nice

Examples

			Table begins:
  1  2  3  4  5  6 ...
  2  3  1  8 10 11 ...
  3  1  2 12 15 13 ...
  4  8 12  6  2 14 ...
		

References

• J. H. Conway, On Numbers and Games, Academic Press, p. 52.

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1830
• H. W. Lenstra, Nim multiplication, (1978)
• Index entries for sequences related to Nim-multiplication

Crossrefs

Cf. A051775, A003987, A051910.

Programs

Maple

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];
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;
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;

Formula

T(n,m) = A051775(n,m).