%I #15 Mar 20 2021 14:40:10

%S 2,3,5,6,7,8,9,11,12,14,15,17,18,19,20,21,23,24,26,27,29,30,32,33,34,

%T 35,36,37,38,39,41,42,43,44,45,47,48,50,51,53,54,56,57,58,59,60,62,63,

%U 65,66,67,68,69,70,71,72,73,74,75,76,77,78,80,81,83,84,85

%N Numbers whose trajectory under iteration of sum of cubes of digits (map) produce a narcissistic number greater than nine.

%C Conjecture: all multiples of 3 are terms of this sequence.

%H J. J. Camacho, <a href="https://www.masscience.com/2020/06/16/un-metodo-insospechado-para-encontrar-numeros-narcisistas/">Un Método Insospechado Para Encontrar Números Narcisistas</a> (in Spanish)

%e For a(1) = 2:

%e 2^3 = 8.

%e 8^3 = 512.

%e 5^3 + 1^3 + 2^3 = 134.

%e 1^3 + 3^3 + 4^3 = 92.

%e 9^3 + 2^3 = 737.

%e 7^3 + 3^3 + 7^3 = 713.

%e 7^3 + 1^3 + 3^3 = 371.

%e 371 is a narcissistic number.

%t (* A example with recurrence formula to test if the number belongs to this sequence *)

%t f[1] = 2;

%t f[n_] := Total[IntegerDigits[f[n - 1]]^3]

%t Table[Total[IntegerDigits[f[n]]^3], {n, 1, 10}]

%Y Cf. A055012 (sum of cubes of digits), A005188 (narcissistic numbers).

%K nonn,base

%O 1,1

%A _José de Jesús Camacho Medina_, Feb 19 2021