A256084 Non-palindromic balanced numbers in base 4.

76, 114, 141, 179, 206, 264, 280, 296, 312, 332, 348, 364, 380, 386, 402, 418, 434, 454, 470, 486, 502, 521, 537, 553, 569, 589, 605, 621, 637, 643, 659, 675, 691, 711, 727, 743, 759, 778, 794, 810, 826, 846, 862, 878, 894, 1060, 1096, 1140, 1176, 1221, 1256, 1320, 1329, 1356, 1400, 1410, 1436, 1481, 1490, 1516, 1554, 1580

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-4 variant of the decimal version A256075 invented by Eric Angelini. See there, and the base-2 version A256082, for further information and examples.

Links

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

Maple

filter:= proc(n) local L, m, i;
  L:= convert(n, base, 4);
  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

Mathematica

A256084Q[k_] := Plus @@ (#*(Range[-#, #] & [(Length[#]-1)/2])) == 0 && !PalindromeQ[#] & [IntegerDigits[k, 4]];
Select[Range[2000], A256084Q] (* Paolo Xausa, Jan 19 2026 *)

Prog

(PARI) is(n, b=4, 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: A330191 A376291 A363352 * A039486 A092890 A261705

Adjacent sequences: A256081 A256082 A256083 * A256085 A256086 A256087

Keyword

nonn,base

Author

M. F. Hasler, Mar 14 2015

Status

approved