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A256081 Non-palindromic balanced primes in base 2. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 18 07:55 EST 2022. Contains 350454 sequences. (Running on oeis4.)