A256081 Non-palindromic balanced primes in base 2.

397, 1427, 1459, 1483, 1613, 1693, 4657, 4721, 4931, 5077, 5273, 5581, 5651, 5749, 6043, 6329, 6637, 6701, 6791, 7127, 7211, 7547, 10069, 10937, 10979, 12011, 12757, 13597, 13789, 18121, 18217, 18307, 18947, 19013, 19141, 19237, 19267, 19813, 19861

Offset: 1

Author

M. F. Hasler, Mar 14 2015

Keywords

• nonn
• base

Comments

Here a number is called balanced if the sum of digits weighted by their arithmetic distance from the "center" is zero. Obviously, all palindromic numbers are balanced; cf. A016041 for base-2 palindromic primes.

These are the primes in A256082. This is the binary variant of the decimal version A256076 suggested by Eric Angelini.

Links

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

Crossrefs

Cf. A016041, A256076, A256075, A256082 - A256089.

Programs

Maple

filter:= proc(n) local L, m;
  L:= convert(n, base, 2);
  m:= (1+nops(L))/2;
  add(L[i]*(i-m), i=1..nops(L))=0 and isprime(n) and L <> ListTools:-Reverse(L)
end proc: select(filter, [seq(i,i=3..20000,2)]);# Robert Israel, May 29 2018

PARI

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