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%I #10 Feb 14 2017 15:04:10
%S 0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,1,1,1,1,2,
%T 2,2,2,2,3,1,1,1,2,2,2,2,3,2,3,1,1,2,2,2,3,2,3,2,3,1,1,2,2,2,2,3,2,3,
%U 3,1,1,2,2,3,3,2,4,3,3,1,1,2,2,2,2,3,3,3,3,1,1,2,3,3,3,3,3,3,2,1,1,1,1,1,1
%N Number of iterations required for the function f(n) to reach a single digit, where f(n) is the product of the two numbers formed from the alternating digits of n.
%C A087471(n) gives the final digit reached by successive iterations of Murthy's function, f(n). A087473(n) gives the smallest number that requires n iterations of Murthy's function to reach a single digit. The n-th row of triangle A087474 gives the n successive iterations of Murthy's function on A087473(n).
%C Differs from A031346 first at n=110. [From _R. J. Mathar_, Sep 11 2008]
%H Robert Israel, <a href="/A087472/b087472.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1234)= 3 since f(1234)=13*24=312, f(312)=32*1=32 and
%e f(32)=3*2=6.
%p murthy:= proc(n) local L,d;
%p L:= convert(n,base,10);
%p d:= nops(L);
%p add(L[2*i+1]*10^i,i=0..(d-1)/2)*add(L[2*i+2]*10^i,i=0..(d-2)/2)
%p end proc:
%p A087472:= proc(n) option remember;
%p if n < 10 then 0 else 1+procname(murthy(n)) fi
%p end proc:
%p map(A087472, [$1..200]); # _Robert Israel_, Feb 14 2017
%Y Cf. A087471, A087473, A087474.
%K nonn,base
%O 1,25
%A _Amarnath Murthy_ and _Paul D. Hanna_, Sep 11 2003
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