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A131184
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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.
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1
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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, 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, 6, 8, 6, 8, 3, 7, 6, 4, 2, 4, 6, 7, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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(.).
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).
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EXAMPLE
| 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).
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MAPLE
| 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:
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:
seq(seq(A131184(n, m), m=1..9), n=1..9) ; # R. J. Mathar, Jul 26 2010
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CROSSREFS
| Sequence in context: A175996 A134982 A064533 * A021933 A154730 A131266
Adjacent sequences: A131181 A131182 A131183 * A131185 A131186 A131187
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KEYWORD
| easy,fini,full,tabf,nonn,less
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AUTHOR
| Philippe Lallouet (philip.lallouet(AT)orange.fr), Oct 20 2007
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EXTENSIONS
| Edited and corrected by R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), Jul 26 2010
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