%I #5 Oct 15 2013 22:32:15

%S 2,6,2,7,2,4,4,2,2,6,6,6,8,6,5,8,8,4,8,2,9,8,6,8,6,2,8,8,2,8,6,2,6,6,

%T 8,2,6,6,6,8,9,2,2,8,2,8,2,8,6,4,2,2,8,8,2,8,6,8,2,8,6,8,9,6,6,2,6,2,

%U 2,2,8,6,8,6,8,2,8,8,8,8,8,8,6,2,6,2,8,6,8,8,8,8,8,6,8,8,6,8,2,8,2,8,6,8,8

%N Fixed point if [nonzero-digit product]-function at initial-value=C[2n,n]=central binomial coefficient is iterated.

%F a(n)=A051802[A000984(n)]=fixed-point of A051801[C(2n, n)]

%e n=10, C[20,10]=184756, iteration list={184756,7560,210,2},

%e a(100)=2.

%t prd[x_] := Apply[Times, DeleteCases[IntegerDigits[x], 0]] Table[FixedPoint[prd, Binomial[2*n, n]], {w, 1, 128}]

%Y Cf. A051801, A051802, A086353-A086361, A029898, A010888, A038194, A000984.

%K base,nonn

%O 1,1

%A _Labos Elemer_, Jul 21 2003