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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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A270824 A048198 A096006 * A131294 A276869 A102313
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Apr 13 2012
STATUS
approved

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Last modified July 19 19:50 EDT 2024. Contains 374436 sequences. (Running on oeis4.)