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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
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
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
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Mar 14 2015
STATUS
approved