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

1,1

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)

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 *)

Prog

(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

Crossrefs

Intersection of A052294 and A144754.

Cf. A089648.

Sequence in context: A242475 A160947 A158581 * A078459 A156345 A078390

Adjacent sequences: A343255 A343256 A343257 * A343259 A343260 A343261

Keyword

nonn,base

Author

Jean-Jacques Vaudroz, Apr 09 2021

Status

approved