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

1,1

Comments

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

Links

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

Example

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

Maple

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

Prog

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

Crossrefs

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

Sequence in context: A345497 A078291 A118216 * A345487 A114838 A036191

Adjacent sequences: A256079 A256080 A256081 * A256083 A256084 A256085

Keyword

nonn,base

Author

M. F. Hasler, Mar 14 2015

Status

approved