A182128 Number of iterations of the map n -> (sum of the decimal digits of n)^3 before reaching the last number of the cycle.

0, 0, 2, 3, 3, 2, 3, 3, 1, 2, 1, 2, 3, 3, 2, 3, 3, 1, 2, 2, 2, 3, 3, 2, 3, 3, 1, 2, 2, 2, 3, 3, 2, 3, 3, 1, 2, 2, 2, 2, 3, 2, 3, 3, 1, 2, 2, 2, 2, 3, 2, 3, 3, 1, 2, 2, 2, 2, 3, 2, 3, 3, 1, 2, 2, 2, 2, 3, 2, 2, 3, 1, 2, 2, 2, 2, 3, 2, 2, 3, 1, 2, 2, 2, 2, 3, 2

Offset

0,3

Comments

a(n) is the number of times that the cube of the sum of the digits must be calculated before reaching the last number of the cycle.

Links

Table of n, a(n) for n=0..86.

Example

0 is in the sequence twice because 0 -> 0 and 1 -> 1;
a(3) = 3:
    3 ->       3^3 = 27;
   27 ->   (2+7)^3 = 729;
  729 -> (7+2+9)^3 = 18^3 = 5832 is the end of the map because 5832 -> (5+8+3+2)^3 = 18^3 is already in the trajectory. Hence we obtain the map: 3 -> 27 -> 729 -> 5832 with 3 iterations.

Maple

A182128 := proc(n)
        local traj , c;
        traj := n ;
        c := [n] ;
        while true do
                traj := A118880(traj) ;
                if member(traj, c) then
                        return nops(c)-1 ;
                end if;
                c := [op(c), traj] ;
        end do:
end proc:
seq(A182128(n), n=0..80) ; # R. J. Mathar, Jul 08 2012

Crossrefs

Cf. A177148, A178481, A118880.

Sequence in context: A270824 A048198 A096006 * A131294 A276869 A102313

Adjacent sequences: A182125 A182126 A182127 * A182129 A182130 A182131

Keyword

nonn,base

Author

Michel Lagneau, Apr 13 2012

Status

approved