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

1,1

Comments

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

Links

Table of n, a(n) for n=1..67.

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

Example

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.

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}]

Crossrefs

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

Sequence in context: A285964 A198045 A152854 * A201144 A095274 A079111

Adjacent sequences: A341760 A341761 A341762 * A341764 A341765 A341766

Keyword

nonn,base

Author

José de Jesús Camacho Medina, Feb 19 2021

Status

approved