A256083 Non-palindromic balanced numbers in base 3.

87, 96, 105, 137, 146, 155, 169, 178, 187, 264, 276, 312, 348, 380, 416, 452, 464, 508, 520, 556, 592, 741, 768, 795, 816, 831, 843, 858, 870, 885, 895, 906, 922, 933, 949, 960, 987, 991, 1014, 1018, 1041, 1045, 1055, 1077, 1082, 1104, 1109, 1131, 1141, 1145, 1168, 1172, 1195, 1199, 1226, 1237, 1253, 1264, 1280, 1291, 1301

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 base-3 variant of the decimal version A256075 invented by Eric Angelini.

All balanced numbers with less than 4 digits are palindromic, and since there is no digit 3 in base 3, there cannot be a term in this sequence with 4 base-3 digits, where weights are (-3/2, -1/2, 1/2, 3/2).

Links

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

Example

a(4) = 137 = 12002[3] is balanced because 1*2 + 2*1 = 0*1 + 2*2.

Maple

filter:= proc(n) local L, m, i;
  L:= convert(n, base, 3);
  m:= (1+nops(L))/2;
add(L[i]*(i-m), i=1..nops(L))=0  and L <> ListTools:-Reverse(L)
end proc:
select(filter, [$1..10000]); # Robert Israel, Nov 04 2024

Prog

(PARI) is(n, b=3, d=digits(n, b), o=(#d+1)/2)=!(vector(#d, i, i-o)*d~)&&d!=Vecrev(d)

Crossrefs

Cf. A256082 - A256089, A256075, A256080.

Sequence in context: A095583 A323414 A231403 * A038005 A305266 A046003

Adjacent sequences: A256080 A256081 A256082 * A256084 A256085 A256086

Keyword

nonn,base

Author

M. F. Hasler, Mar 14 2015

Status

approved