A341763 Numbers whose trajectory under iteration of sum of cubes of digits (map) produce a narcissistic number greater than nine.

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, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57, 58, 59, 60, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81, 83, 84, 85

Offset: 1

Author

José de Jesús Camacho Medina, Feb 19 2021

Keywords

• nonn
• base

Comments

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

Examples

			For a(1) = 2:
2^3 = 8.
8^3 = 512.
5^3 + 1^3 + 2^3 = 134.
1^3 + 3^3 + 4^3 = 92.
9^3 + 2^3 = 737.
7^3 + 3^3 + 7^3 = 713.
7^3 + 1^3 + 3^3 = 371.
371 is a narcissistic number.
		

Links

• J. J. Camacho, Un Método Insospechado Para Encontrar Números Narcisistas (in Spanish)

Crossrefs

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

Programs

Mathematica

(* A example with recurrence formula to test if the number belongs to this sequence *)
f[1] = 2;
f[n_] := Total[IntegerDigits[f[n - 1]]^3]
Table[Total[IntegerDigits[f[n]]^3], {n, 1, 10}]