A343258 Numbers whose binary representation has a prime number of zeros and a prime number of ones.

9, 10, 12, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 35, 37, 38, 41, 42, 44, 49, 50, 52, 56, 65, 66, 68, 72, 79, 80, 87, 91, 93, 94, 96, 103, 107, 109, 110, 115, 117, 118, 121, 122, 124, 131, 133, 134, 137, 138, 140, 143, 145, 146, 148, 151, 152, 155, 157, 158

Offset: 1

Author

Jean-Jacques Vaudroz, Apr 09 2021

Keywords

• nonn
• base

Comments

Terms of 4, 5 and 6 total bits (9 through 56) are the same as A089648.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 78 terms from Jean-Jacques Vaudroz)

Crossrefs

Intersection of A052294 and A144754.

Cf. A089648.

Programs

Maple

q:= n->(l->(t->andmap(isprime, [t, nops(l)-t]))(add(i, i=l)))(Bits[Split](n)):
select(q, [$1..200])[];  # Alois P. Heinz, Apr 11 2021

Mathematica

Select[Range[160], And @@ PrimeQ[DigitCount[#, 2]] &] (* Amiram Eldar, Apr 09 2021 *)

PARI

isa(n)= isprime(hammingweight(n));
isb(n)= isprime(#binary(n) - hammingweight(n));
isok(n) = isa(n) && isb(n);

Python

from sympy import isprime
def ok(n): b = bin(n)[2:]; return all(isprime(b.count(d)) for d in "01")
print(list(filter(ok, range(159)))) # Michael S. Branicky, Sep 10 2021