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

Author

M. F. Hasler, Mar 14 2015

Keywords

• nonn
• base

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).

Examples

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

Links

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

Crossrefs

Cf. A256082 - A256089, A256075, A256080.

Programs

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

PARI

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