login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A256083
Non-palindromic balanced numbers in base 3.
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
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