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

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, 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, 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

Offset: 0

Author

Michel Lagneau, May 03 2010

Keywords

• nonn
• base

Comments

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.

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.

Examples

			0 is in the sequence twice because 0->0 and 1 -> 1 ;
5 is in the sequence because : 5 -> 25 -> 49 -> 169 -> 256, last number because 256 -> 169.
		

Crossrefs

Cf. A118881.

Programs

Maple

A177148 := proc(n)
        local traj ,a,m,c;
        traj := n ;
        c := [n] ;
        while true do
                traj := A118881(traj) ;
                if member(traj,c) then
                        return nops(c)-1 ;
                end if;
                c := [op(c),traj] ;
        end do:
end proc: # R. J. Mathar, Jul 08 2012