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A182111 Number of iterations of the map n -> sum of the cubes of the decimal digits of n. 1
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

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, A152077, A160862.

Sequence in context: A215693 A197028 A257819 * A023643 A050009 A173182

Adjacent sequences:  A182108 A182109 A182110 * A182112 A182113 A182114

KEYWORD

nonn,base

AUTHOR

Michel Lagneau, Apr 12 2012

STATUS

approved

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Last modified July 11 17:52 EDT 2020. Contains 335626 sequences. (Running on oeis4.)