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

Author

Joseph Myers, Jun 28 2009

Keywords

• base
• nonn

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)

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).

Programs

PARI

select( {is_A162225(n, b=6)=if(n1 && 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