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

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

Offset: 1

Author

Michel Lagneau, Apr 12 2012

Keywords

• nonn
• base

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).

Examples

			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.
		

Crossrefs

Cf. A000578, A055012, A152077, A160862, A165331.

Programs

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:
seq(a(n), n=1..85);  # Alois P. Heinz, Mar 01 2018