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 A256082 Non-palindromic balanced numbers in base 2. 12
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified January 28 23:06 EST 2022. Contains 350670 sequences. (Running on oeis4.)