A256085 -id:A256085 - cp's OEIS frontend

A256082 Non-palindromic balanced numbers in base 2.

70, 78, 150, 266, 282, 294, 310, 334, 350, 355, 371, 397, 413, 540, 554, 582, 630, 686, 723, 798, 813, 1036, 1042, 1068, 1074, 1098, 1116, 1130, 1148, 1158, 1178, 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

Offset: 1

M. F. Hasler, Mar 14 2015

Here a number is called balanced if the sum of digits weighted by their arithmetic distance from the "center" is zero.
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.
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

			a(1) = 70 = 1000110[2] is balanced because 1*3 = 1*1 + 1*2.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A256081 (primes), A256083, A256084, A256085, A256086, A256087, A256088, A256089, A256075.

filter:= proc(n) local L,m;
  L:= convert(n,base,2);
  m:= (1+nops(L))/2;
  add(L[i]*(i-m),i=1..nops(L))=0 and L <> ListTools:-Reverse(L)
end proc:
select(filter, [$2..10000]); # Robert Israel, May 29 2018

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

cp's OEIS Frontend

A256082 Non-palindromic balanced numbers in base 2.

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