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A256084 Non-palindromic balanced numbers in base 4.

%I A256084 #9 Nov 04 2024 18:33:32
%S A256084 76,114,141,179,206,264,280,296,312,332,348,364,380,386,402,418,434,
%T A256084 454,470,486,502,521,537,553,569,589,605,621,637,643,659,675,691,711,
%U A256084 727,743,759,778,794,810,826,846,862,878,894,1060,1096,1140,1176,1221,1256,1320,1329,1356,1400,1410,1436,1481,1490,1516,1554,1580
%N A256084 Non-palindromic balanced numbers in base 4.
%C A256084 Here a number is called balanced if the sum of digits weighted by their arithmetic distance from the "center" is zero.
%C A256084 This is the base-4 variant of the decimal version A256075 invented by Eric Angelini. See there, and the base-2 version A256082, for further information and examples.
%H A256084 Robert Israel, <a href="/A256084/b256084.txt">Table of n, a(n) for n = 1..10000</a>
%p A256084 filter:= proc(n) local L, m,i;
%p A256084   L:= convert(n, base, 4);
%p A256084   m:= (1+nops(L))/2;
%p A256084 add(L[i]*(i-m), i=1..nops(L))=0  and L <> ListTools:-Reverse(L)
%p A256084 end proc:
%p A256084 select(filter, [$1..10000]); # _Robert Israel_, Nov 04 2024
%o A256084 (PARI) is(n,b=4,d=digits(n,b),o=(#d+1)/2)=!(vector(#d,i,i-o)*d~)&&d!=Vecrev(d)
%Y A256084 Cf. A256082 - A256089, A256075, A256080.
%K A256084 nonn,base
%O A256084 1,1
%A A256084 _M. F. Hasler_, Mar 14 2015