A162225 - OEIS

%I #15 Jan 17 2020 14:06:23

%S 0,1,2,3,4,5,99,190,251,308,2292,2293,2324,3432,3433,6197,36140,

%T 269458,391907,10067135,1428423394,2510142206,2511720147,3866632806,

%U 3866632807,3930544834,4953134588,5018649129,6170640875,32693825124,32693825125

%N 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.

%C 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

%H Joseph Myers, <a href="/A162225/b162225.txt">Table of n, a(n) for n = 1..764</a> (complete to 350 base-6 digits)

%o (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

%Y 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).

%K base,nonn

%O 1,3

%A _Joseph Myers_, Jun 28 2009