

A182111


Number of iterations of the map n > sum of the cubes of the decimal digits of n.


2



1, 7, 3, 6, 6, 10, 6, 6, 4, 1, 8, 5, 5, 6, 10, 3, 8, 2, 2, 7, 5, 4, 7, 3, 3, 8, 2, 4, 3, 3, 5, 7, 6, 3, 6, 6, 1, 8, 6, 6, 6, 3, 3, 7, 5, 5, 1, 6, 4, 6, 10, 3, 6, 5, 3, 5, 5, 8, 10, 10, 3, 8, 6, 5, 5, 6, 7, 11, 6, 6, 8, 2, 1, 1, 5, 7, 7, 8, 4, 6, 2, 4, 8, 6, 8
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

a(n) is the number of times you obtain the sums of cubes of digits of n before reaching a fixed point (last number of the cycle).


LINKS



EXAMPLE

a(3) = 3 because :
3^3 = 27 > 2^3 + 7^3 = 351;
351 > 3^3 + 5^3 + 1^3 = 153;
153 > 1^3+5^3+3^3 = 153 is the end because this number is already in the trajectory. Hence we obtain the map : 3 > 27 > 351 > 153 with 3 iterations.


MAPLE

a:= proc(n) local k, m, s; m:= n; s:= {};
for k from 0 do
m:= add(i^3, i=convert(m, base, 10));
if m in s then return k fi;
s:= s union {m}
od
end:


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



