A256089 - OEIS

%I #9 Nov 04 2024 18:33:18

%S 756,846,936,974,1026,1064,1116,1154,1206,1218,1244,1308,1334,1398,

%T 1424,1486,1512,1576,1602,1666,1692,1704,1756,1794,1846,1884,1936,

%U 1948,1974,2038,2064,2128,2154,2216,2242,2306,2332,2396,2422,2434,2486,2524,2576,2614,2666,2678,2704,2768,2794,2858,2884,2946,2972

%N Non-palindromic balanced numbers in base 9.

%C Here a number is called balanced if the sum of digits weighted by their arithmetic distance from the "center" is zero. Since palindromes (A029955) are trivially balanced, they are excluded here.

%C This is the base-9 variant of the decimal version A256075 invented by Eric Angelini. See there, and the base-2 version A256082, for further information and examples.

%H Robert Israel, <a href="/A256089/b256089.txt">Table of n, a(n) for n = 1..10000</a>

%p filter:= proc(n) local L, m,i;

%p   L:= convert(n, base, 9);

%p   m:= (1+nops(L))/2;

%p add(L[i]*(i-m), i=1..nops(L))=0  and L <> ListTools:-Reverse(L)

%p end proc:

%p select(filter, [$1..10000]); # _Robert Israel_, Nov 04 2024

%o (PARI) is(n,b=9,d=digits(n,b),o=(#d+1)/2)=!(vector(#d,i,i-o)*d~)&&d!=Vecrev(d)

%Y Cf. A256082 - A256088, A256075, A256080, A029955.

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Mar 14 2015