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A256075 Non-palindromic balanced numbers (in base 10).

%I A256075 #17 Dec 23 2024 14:53:44
%S A256075 1030,1140,1250,1302,1360,1412,1470,1522,1580,1603,1632,1690,1713,
%T A256075 1742,1823,1852,1904,1933,1962,2031,2060,2141,2170,2251,2280,2303,
%U A256075 2361,2390,2413,2471,2523,2581,2604,2633,2691,2714,2743,2824,2853,2905,2934,2963,3032,3061,3090,3142,3171,3252,3281,3304,3362,3391,3414
%N A256075 Non-palindromic balanced numbers (in base 10).
%C A256075 Here a number is called balanced if the sum of digits weighted by their arithmetic distance from the "center" is zero.
%C A256075 All 1-, 2- or 3-digit balanced numbers are palindromic, therefore all terms are larger than 1000.
%C A256075 The least 1-9 pandigital balanced number seems to be 137986542, but there seems to be no 0-9 pandigital balanced number.
%H A256075 Robert Israel, <a href="/A256075/b256075.txt">Table of n, a(n) for n = 1..10000</a>
%H A256075 E. Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2015-March/014585.html">Balanced numbers</a>, SeqFan list, Mar 14 2015
%e A256075 a(1)=1030 is balanced because 1*3/2 + 0*1/2 = 3*1/2 + 0*3/2.
%e A256075 a(2)=1140 is balanced because 1*3/2 + 1*1/2 = 4*1/2 + 0*3/2.
%p A256075 filter:= proc(n) local L,m;
%p A256075   L:= convert(n,base,10);
%p A256075   m:= (1+nops(L))/2;
%p A256075 add(L[i]*(i-m),i=1..nops(L))=0  and L <> ListTools:-Reverse(L)
%p A256075 end proc:
%p A256075 select(filter, [$1000..10000]); # _Robert Israel_, May 29 2018
%o A256075 (PARI) is(n,b=10,d=digits(n,b),o=(#d+1)/2)=!(vector(#d,i,i-o)*d~)&&d!=Vecrev(d)
%Y A256075 Cf. A256076 (primes in this sequence), A256082 - A256089, A256080.
%K A256075 nonn,base
%O A256075 1,1
%A A256075 _Eric Angelini_ and _M. F. Hasler_, Mar 14 2015