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%I #14 Nov 22 2019 01:31:17
%S 0,1,2,3,8,9,28,29,32,33,35,43,55,62,83,128,129,243,512,513,922,2048,
%T 2049,2316,2317,2444,2445,2571,2699,7330,8192,8193,13124,13125,20710,
%U 21222,32768,32769,40392,40393,131072,131073,524288,524289,1075174
%N Base 4 perfect digital invariants (written in base 10): numbers equal to the sum of the k-th powers of their base-4 digits, for some k.
%C Whenever a(n) is a multiple of 4, then a(n+1) = a(n) + 1 is also a base 4 perfect digital invariant, with the same exponent k. - _M. F. Hasler_, Nov 21 2019
%H Joseph Myers, <a href="/A162219/b162219.txt">Table of n, a(n) for n=1..6778</a> (complete to 1500 base 4 digits)
%o (PARI) select( {is_A162219(n, b=4)=n<b||forstep(k=logint(n, max(vecmax(b=digits(n, b)), 2)), 2, -1, my(s=vecsum([d^k|d<-b])); s>n||return(s==n))}, [0..10^5]) \\ _M. F. Hasler_, Nov 21 2019
%Y Cf. A162220 (corresponding exponents), A010344 (restriction to power = number of digits), A033836, A162221. In other bases: A162216 (base 3), A162222 (base 5), A162225 (base 6), A162228 (base 7), A162231 (base 8), A162234 (base 9), A023052 (base 10).
%K base,nonn
%O 1,3
%A _Joseph Myers_, Jun 28 2009
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