A162234 Base 9 perfect digital invariants (written in base 10): numbers equal to the sum of the k-th powers of their base-9 digits, for some k.

0, 1, 2, 3, 4, 5, 6, 7, 8, 27, 28, 41, 50, 126, 127, 243, 244, 353, 468, 469, 1052, 1824, 2187, 2188, 8052, 8295, 9857, 19683, 19684, 36804, 65538, 65539, 177147, 177148, 1198372, 1594323, 1594324, 3357009, 3357010, 5300099, 6287267, 10097892

Offset

1,3

Comments

Whenever a(n) is a multiple of 9, then a(n+1) = a(n) + 1 is also a base 9 perfect digital invariant, with the same exponent k. - M. F. Hasler, Nov 21 2019

Links

Joseph Myers, Table of n, a(n) for n=1..506 (complete to 120 base 9 digits)

Prog

(PARI) select( {is_A162234(n, b=9)=n<b|| forstep(p=logint(n, max(vecmax(b=digits(n, b)), 2)), 2, -1, my(t=vecsum([d^p|d<-b])); t>n|| return(t==n))}, [0..10^5]) \\ M. F. Hasler, Nov 21 2019

Crossrefs

Cf. A162235 (corresponding exponents), A010353 (restriction to power = number of digits), A033841, A162236. In other bases: A162216 (base 3), A162219 (base 4), A162222 (base 5), A162225 (base 6), A162228 (base 7), A162231 (base 8), A023052 (base 10).

Sequence in context: A335900 A096986 A031097 * A024651 A004848 A183531

Adjacent sequences: A162231 A162232 A162233 * A162235 A162236 A162237

Keyword

base,nonn

Author

Joseph Myers, Jun 28 2009

Status

approved