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A256082 Non-palindromic balanced numbers in base 2.

%I A256082 #13 May 29 2018 14:27:14
%S A256082 70,78,150,266,282,294,310,334,350,355,371,397,413,540,554,582,630,
%T A256082 686,723,798,813,1036,1042,1068,1074,1098,1116,1130,1148,1158,1178,
%U A256082 1190,1210,1221,1238,1253,1270,1302,1305,1334,1337,1347,1358,1379,1390,1427,1438,1459,1470,1483,1515,1550,1557,1582,1589,1613,1630
%N A256082 Non-palindromic balanced numbers in base 2.
%C A256082 Here a number is called balanced if the sum of digits weighted by their arithmetic distance from the "center" is zero.
%C A256082 This is the binary variant of the base-10 version A256075 invented by Eric Angelini. See A256081 for the primes in this sequence. See A256083 - A256089 and A256080 for variants in other bases.
%C A256082 If n is in the sequence with 2^d < n < 2^(d+1), then 2^(d+2)+2*n+1 is in the sequence, as are n*(2^k+1) for k > d. - _Robert Israel_, May 29 2018
%H A256082 Robert Israel, <a href="/A256082/b256082.txt">Table of n, a(n) for n = 1..10000</a>
%e A256082 a(1) = 70 = 1000110[2] is balanced because 1*3 = 1*1 + 1*2.
%p A256082 filter:= proc(n) local L,m;
%p A256082   L:= convert(n,base,2);
%p A256082   m:= (1+nops(L))/2;
%p A256082   add(L[i]*(i-m),i=1..nops(L))=0 and L <> ListTools:-Reverse(L)
%p A256082 end proc:
%p A256082 select(filter, [$2..10000]); # _Robert Israel_, May 29 2018
%o A256082 (PARI) is(n,b=2,d=digits(n,b),o=(#d+1)/2)=!(vector(#d,i,i-o)*d~)&&d!=Vecrev(d)
%Y A256082 Cf. A256081 (primes), A256083, A256084, A256085, A256086, A256087, A256088, A256089, A256075.
%K A256082 nonn,base
%O A256082 1,1
%A A256082 _M. F. Hasler_, Mar 14 2015