A256090 Non-palindromic balanced primes in base 16.

6451, 7717, 8513, 8963, 9601, 10501, 10867, 11317, 11411, 12227, 13829, 14561, 15461, 15733, 16183, 16529, 16979, 18517, 19333, 19427, 19699, 20149, 20233, 20327, 22483, 22567, 23027, 23561, 23833, 25717, 26083, 26261, 26711, 27077, 27527, 27799, 27893, 28867, 29411, 29683, 30133, 30677, 30949, 31033, 31849

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. Palindromic primes (A029732 in base 16) are trivially balanced, therefore they are excluded here.

These are the primes in A256080. This is the hexadecimal variant of the decimal version A256076 suggested by Eric Angelini.

Links

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

Mathematica

A256090Q[p_] := Plus @@ (#*(Range[-#, #] & [(Length[#]-1)/2])) == 0 && !PalindromeQ[#] & [IntegerDigits[p, 16]];
Select[Prime[Range[3500]], A256090Q] (* 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)&&isprime(n)

Crossrefs

Cf. A256080, A256076, A256075, A256082 - A256089, A029732.

Sequence in context: A074978 A105377 A248998 * A383318 A067928 A166223

Adjacent sequences: A256087 A256088 A256089 * A256091 A256092 A256093

Keyword

nonn,base

Author

M. F. Hasler, Mar 14 2015

Status

approved