A162225 Base-6 perfect digital invariants (written in base 10): numbers equal to the sum of the k-th powers of their base-6 digits, for some k.

0, 1, 2, 3, 4, 5, 99, 190, 251, 308, 2292, 2293, 2324, 3432, 3433, 6197, 36140, 269458, 391907, 10067135, 1428423394, 2510142206, 2511720147, 3866632806, 3866632807, 3930544834, 4953134588, 5018649129, 6170640875, 32693825124, 32693825125

Offset

1,3

Comments

Whenever a(n) is a multiple of 6, then a(n+1) = a(n) + 1 is also a base-6 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..764 (complete to 350 base-6 digits)

Prog

(PARI) select( {is_A162225(n, b=6)=if(n<b, 1, my(t=vecmax(b=digits(n, b))); t>1 && forstep(p=logint(n, t), logint(n, vecsum(b)), -1, (t=vecsum([d^p|d<-b]))>n|| return(t==n)))}, [0..10^5]) \\ M. F. Hasler, Nov 21 2019

Crossrefs

Cf. A162226 (corresponding exponents), A010348 (restriction to power = number of digits), A033838, A162227. In other bases: A162216 (base 3), A162219 (base 4), A162222 (base 5), A162228 (base 7), A162231 (base 8), A162234 (base 9), A023052 (base 10).

Sequence in context: A374431 A334536 A097931 * A010348 A171591 A140432

Adjacent sequences: A162222 A162223 A162224 * A162226 A162227 A162228

Keyword

base,nonn

Author

Joseph Myers, Jun 28 2009

Status

approved