A162216 Base-3 perfect digital invariants (written in base 10): numbers equal to the sum of the k-th powers of their base-3 digits, for some k.

0, 1, 2, 5, 8, 17, 33, 34, 65, 66, 67, 131, 258, 259, 386, 512, 513, 514, 1026, 1027, 2049, 2050, 3075, 3076, 4100, 16388, 16389, 16390, 57345, 57346, 65538, 65539, 196610, 262149, 262150, 458754, 458755, 786438, 786439, 1048581, 1048582, 1310724

Offset: 1

Author

Joseph Myers, Jun 28 2009

Keywords

• base
• nonn

Comments

Whenever 3|a(n), then a(n+1) = a(n) + 1 (for the same k). The first 6 terms are exactly all the base-3 narcissistic numbers (where k = number of base-3 digits). For these numbers in other bases b = 4, ..., 16 see A010344 - A161953. - M. F. Hasler, Nov 18 2019

Links

• Joseph Myers, Table of n, a(n) for n = 1..6130 (complete to 2000 base-3 digits)

Crossrefs

Cf. A162217 (corresponding exponents), A033835, A162218. In other bases: A162219 (base 4), A162222 (base 5), A162225 (base 6), A162228 (base 7), A162231 (base 8), A162234 (base 9), A023052 (base 10).

Programs

PARI

select( is_A162216(n,b=3)={nn||return(s==n))}, [0..10^5]) \\ M. F. Hasler, Nov 21 2019