A131184 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.

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

Offset

1,2

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).

Links

Table of n, a(n) for n=1..81.

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).

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

Crossrefs

Sequence in context: A248940 A134982 A064533 * A021933 A154730 A242967

Adjacent sequences: A131181 A131182 A131183 * A131185 A131186 A131187

Keyword

easy,fini,full,tabf,nonn,less

Author

Philippe Lallouet (philip.lallouet(AT)orange.fr), Oct 20 2007

Extensions

Edited and corrected by R. J. Mathar, Jul 26 2010

Status

approved