

A182128


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


4



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
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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



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

local traj , c;
traj := n ;
c := [n] ;
while true do
if member(traj, c) then
return nops(c)1 ;
end if;
c := [op(c), traj] ;
end do:
end proc:


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



