A343258 - OEIS

%I #32 Sep 10 2021 10:47:58

%S 9,10,12,17,18,19,20,21,22,24,25,26,28,35,37,38,41,42,44,49,50,52,56,

%T 65,66,68,72,79,80,87,91,93,94,96,103,107,109,110,115,117,118,121,122,

%U 124,131,133,134,137,138,140,143,145,146,148,151,152,155,157,158

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

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

%H Alois P. Heinz, <a href="/A343258/b343258.txt">Table of n, a(n) for n = 1..10000</a> (first 78 terms from Jean-Jacques Vaudroz)

%p q:= n->(l->(t->andmap(isprime, [t, nops(l)-t]))(add(i, i=l)))(Bits[Split](n)):

%p select(q, [$1..200])[];  # _Alois P. Heinz_, Apr 11 2021

%t Select[Range[160], And @@ PrimeQ[DigitCount[#, 2]] &] (* _Amiram Eldar_, Apr 09 2021 *)

%o (PARI)

%o isa(n)= isprime(hammingweight(n));

%o isb(n)= isprime(#binary(n) - hammingweight(n));

%o isok(n) = isa(n) && isb(n);

%o (Python)

%o from sympy import isprime

%o def ok(n): b = bin(n)[2:]; return all(isprime(b.count(d)) for d in "01")

%o print(list(filter(ok, range(159)))) # _Michael S. Branicky_, Sep 10 2021

%Y Intersection of A052294 and A144754.

%Y Cf. A089648.

%K nonn,base

%O 1,1

%A _Jean-Jacques Vaudroz_, Apr 09 2021