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A177148 a(n) = number of squares of summations of digits before reaching the end of the cycle.

%I A177148 #4 Jul 08 2012 13:04:34
%S A177148 0,0,5,2,4,4,2,3,3,1,1,5,2,4,4,2,3,3,1,2,5,2,4,4,2,3,3,1,2,5,2,4,4,2,
%T A177148 3,3,1,2,5,2,4,4,2,3,3,1,2,5,2,2,4,2,3,3,1,2,5,2,2,3,2,3,3,1,2,5,2,2,
%U A177148 3,2,3,3,1,2,5,2,2,3,2,2,3,1,2,5,2,2,3,2,2,4,1,2,5,2,2,3,2,2,4,2,1,5,2,4,4
%N A177148 a(n) = number of squares of summations of digits before reaching the end of the cycle.
%C A177148 a(n) is the number of times you form the square of the sum of the digits before reaching the last number of the cycle. According to the computations with Maple program, this last number belong to the set {1,81,100,169,256}, and a(n) < = 5.
%C A177148 Example : 4 -> 16 -> (1+6)^2 = 49 -> (4+9)^2 = 169 -> (1+6+9)^2 = 256, and 256 is the last number of the list because 256 -> (2+5+6)^2 = 169 belong to the list.
%e A177148 0 is in the sequence twice because 0->0 and 1 -> 1 ;
%e A177148 5 is in the sequence because : 5 -> 25 -> 49 -> 169 -> 256, last number because 256 -> 169.
%p A177148 A177148 := proc(n)
%p A177148         local traj ,a,m,c;
%p A177148         traj := n ;
%p A177148         c := [n] ;
%p A177148         while true do
%p A177148                 traj := A118881(traj) ;
%p A177148                 if member(traj,c) then
%p A177148                         return nops(c)-1 ;
%p A177148                 end if;
%p A177148                 c := [op(c),traj] ;
%p A177148         end do:
%p A177148 end proc: # _R. J. Mathar_, Jul 08 2012
%Y A177148 Cf. A118881.
%K A177148 nonn,base
%O A177148 0,3
%A A177148 _Michel Lagneau_, May 03 2010