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A256083 Non-palindromic balanced numbers in base 3.

%I A256083 #11 Nov 04 2024 18:34:02
%S A256083 87,96,105,137,146,155,169,178,187,264,276,312,348,380,416,452,464,
%T A256083 508,520,556,592,741,768,795,816,831,843,858,870,885,895,906,922,933,
%U A256083 949,960,987,991,1014,1018,1041,1045,1055,1077,1082,1104,1109,1131,1141,1145,1168,1172,1195,1199,1226,1237,1253,1264,1280,1291,1301
%N A256083 Non-palindromic balanced numbers in base 3.
%C A256083 Here a number is called balanced if the sum of digits weighted by their arithmetic distance from the "center" is zero.
%C A256083 This is the base-3 variant of the decimal version A256075 invented by Eric Angelini.
%C A256083 All balanced numbers with less than 4 digits are palindromic, and since there is no digit 3 in base 3, there cannot be a term in this sequence with 4 base-3 digits, where weights are (-3/2, -1/2, 1/2, 3/2).
%H A256083 Robert Israel, <a href="/A256083/b256083.txt">Table of n, a(n) for n = 1..10000</a>
%e A256083 a(4) = 137 = 12002[3] is balanced because 1*2 + 2*1 = 0*1 + 2*2.
%p A256083 filter:= proc(n) local L, m,i;
%p A256083   L:= convert(n, base, 3);
%p A256083   m:= (1+nops(L))/2;
%p A256083 add(L[i]*(i-m), i=1..nops(L))=0  and L <> ListTools:-Reverse(L)
%p A256083 end proc:
%p A256083 select(filter, [$1..10000]); # _Robert Israel_, Nov 04 2024
%o A256083 (PARI) is(n,b=3,d=digits(n,b),o=(#d+1)/2)=!(vector(#d,i,i-o)*d~)&&d!=Vecrev(d)
%Y A256083 Cf. A256082 - A256089, A256075, A256080.
%K A256083 nonn,base
%O A256083 1,1
%A A256083 _M. F. Hasler_, Mar 14 2015