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

1,1

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

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

Prog

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

Crossrefs

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

Sequence in context: A341187 A038660 A129190 * A338476 A152309 A298124

Adjacent sequences: A256078 A256079 A256080 * A256082 A256083 A256084

Keyword

nonn,base

Author

M. F. Hasler, Mar 14 2015

Status

approved