cp's OEIS Frontend

A182111 Number of iterations of the map n -> sum of the cubes of the decimal digits of n.

%I A182111 #18 Jan 28 2022 09:48:47
%S A182111 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,
%T A182111 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,
%U A182111 7,11,6,6,8,2,1,1,5,7,7,8,4,6,2,4,8,6,8
%N A182111 Number of iterations of the map n -> sum of the cubes of the decimal digits of n.
%C A182111 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).
%e A182111 a(3) = 3 because :
%e A182111 3^3  = 27 -> 2^3 + 7^3 = 351;
%e A182111 351 -> 3^3 + 5^3 + 1^3 = 153;
%e A182111 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.
%p A182111 a:= proc(n) local k, m, s; m:= n; s:= {};
%p A182111       for k from 0 do
%p A182111         m:= add(i^3, i=convert(m, base, 10));
%p A182111         if m in s then return k fi;
%p A182111         s:= s union {m}
%p A182111       od
%p A182111     end:
%p A182111 seq(a(n), n=1..85);  # _Alois P. Heinz_, Mar 01 2018
%Y A182111 Cf. A000578, A055012, A152077, A160862, A165331.
%K A182111 nonn,base
%O A182111 1,2
%A A182111 _Michel Lagneau_, Apr 12 2012