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A256086 Non-palindromic balanced numbers in base 6.

%I A256086 #9 Nov 04 2024 18:34:17
%S A256086 234,276,318,326,368,410,451,493,535,543,585,627,668,710,752,760,802,
%T A256086 844,885,927,969,977,1019,1061,1102,1144,1186,1308,1344,1380,1416,
%U A256086 1452,1488,1530,1566,1602,1638,1674,1710,1730,1752,1766,1788,1802,1824,1838,1860,1874,1896,1910,1932,1952,1974,1988
%N A256086 Non-palindromic balanced numbers in base 6.
%C A256086 Here a number is called balanced if the sum of digits weighted by their arithmetic distance from the "center" is zero. Since palindromes (A029953) are trivially balanced, they are excluded here.
%C A256086 This is the base-6 variant of the decimal version A256075 invented by Eric Angelini. See there, and the base-2 version A256082, for further information and examples.
%H A256086 Robert Israel, <a href="/A256086/b256086.txt">Table of n, a(n) for n = 1..10000</a>
%p A256086 filter:= proc(n) local L, m,i;
%p A256086   L:= convert(n, base, 6);
%p A256086   m:= (1+nops(L))/2;
%p A256086 add(L[i]*(i-m), i=1..nops(L))=0  and L <> ListTools:-Reverse(L)
%p A256086 end proc:
%p A256086 select(filter, [$1..10000]); # _Robert Israel_, Nov 04 2024
%o A256086 (PARI) is(n,b=6,d=digits(n,b),o=(#d+1)/2)=!(vector(#d,i,i-o)*d~)&d!=Vecrev(d)
%Y A256086 Cf. A256082 - A256089, A256075, A256076, A256080, A029953.
%K A256086 nonn,base
%O A256086 1,1
%A A256086 _M. F. Hasler_, Mar 14 2015