A256080 Non-palindromic balanced numbers in base 16.

4144, 4416, 4688, 4866, 4960, 5138, 5232, 5410, 5504, 5635, 5682, 5776, 5907, 5954, 6048, 6179, 6226, 6320, 6404, 6451, 6498, 6592, 6676, 6723, 6770, 6864, 6948, 6995, 7042, 7136, 7173, 7220, 7267, 7314, 7408, 7445, 7492, 7539, 7586, 7717, 7764, 7811, 7858, 7942, 7989

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. Palindromes (A029730) are trivially balanced, therefore they are excluded here.

This is the hexadecimal variant of the decimal version A256075 invented by Eric Angelini. See there, and the base-2 version A256082, for further information and examples. See A256090 for the primes in this sequence.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Mathematica

A256080Q[k_] := Plus @@ (#*(Range[-#, #] & [(Length[#]-1)/2])) == 0 && !PalindromeQ[#] & [IntegerDigits[k, 16]];
Select[Range[8000], A256080Q] (* Paolo Xausa, Jan 20 2026 *)

Prog

(PARI) is(n, b=16, d=digits(n, b), o=(#d+1)/2)=!(vector(#d, i, i-o)*d~)&&d!=Vecrev(d)

Crossrefs

Cf. A256082 - A256089, A256075, A256076, A256090.

Sequence in context: A107541 A254230 A106537 * A287514 A072896 A052464

Adjacent sequences: A256077 A256078 A256079 * A256081 A256082 A256083

Keyword

nonn,base

Author

M. F. Hasler, Mar 14 2015

Status

approved