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%I #10 Jan 21 2013 09:58:31
%S 1,7,6,4,2,2,6,7,3,8,6,8,6,3,6,8,6,8,6,7,6,7,2,7,6,7,6,5,6,8,3,3,3,8,
%T 6,5,3,3,3,3,1,3,3,3,3,3,6,8,3,3,1,8,6,5,6,7,6,7,2,7,6,7,6,8,6,8,6,3,
%U 6,8,6,8,3,7,6,4,2,4,6,7,3
%N Table T(n,m): the length of the sequence b(1)=n, b(2)=m, b(i) = b(i-1)*b(i-2) mod 10 up to the end of b's first cycle.
%C For each of the rows 1<=n<=9 and columns 1<=m<=9 of the table, an auxiliary sequence b(.) is initialized with n and m. Further terms of b are defined by the last digit of the product of the previous two terms of b(.).
%C Each of these 81 sequences b(.) enters a cycle, and the length of b(.) measured up to the end of the first cycle defines T(n,m).
%e For n=1, m=8, the sequence is b(.) = 1, 8, 8, 4, 2, 8, 6, [8, 8, 4, 2, 8, 6, ...], with T(1,8) = 7 numbers prior to the re-entering the cycle (cycle in brackets).
%p cyc := proc(L) for i from 2 to nops(L) do for j from 1 to i-1 do if op(j,L) = op(i,L) and op(j+1,L) = op(i+1,L) then return i-1 ; end if; end do: end do; return -1 ; end proc:
%p A131184 := proc(n,m) b := [n,m] ; for i from 3 to 30 do b := [op(b), (op(-1,b)*op(-2,b)) mod 10] ; end do: return cyc(b) ; end proc:
%p seq(seq(A131184(n,m),m=1..9),n=1..9) ; # _R. J. Mathar_, Jul 26 2010
%K easy,fini,full,tabf,nonn,less
%O 1,2
%A Philippe Lallouet (philip.lallouet(AT)orange.fr), Oct 20 2007
%E Edited and corrected by _R. J. Mathar_, Jul 26 2010
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