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
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Mar 14 2015
STATUS
approved