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

1,2

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

Table of n, a(n) for n=1..85.

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

Crossrefs

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

Sequence in context: A215693 A197028 A257819 * A344916 A023643 A050009

Adjacent sequences: A182108 A182109 A182110 * A182112 A182113 A182114

Keyword

nonn,base

Author

Michel Lagneau, Apr 12 2012

Status

approved