%I #29 Dec 27 2023 16:15:48

%S 17,19,37,41,43,53,71,79,83,89,101,103,107,109,113,131,137,151,157,

%T 167,173,179,181,193,199,211,227,229,233,241,257,263,269,277,281,293,

%U 311,317,337,347,349,353,359,367,373,379,389,401,431,439,443,449,461,463

%N Primes with a prime number of 0's in their binary representations.

%H Robert Israel, <a href="/A144213/b144213.txt">Table of n, a(n) for n = 1..10000</a>

%e 41, a prime, in binary is 101001. This has three 0's and 3 is prime, so 41 is in the sequence.

%p A080791 := proc(n) local i,dgs ; dgs := convert(n,base,2) ; nops(dgs)-add(i,i=dgs) ; end: isA144213 := proc(n) local no0 ; no0 := A080791(n) ; if isprime(n) and isprime(no0) then true ; else false; fi; end: for n from 1 to 1200 do if isA144213(n) then printf("%d,",n) ; fi; od: # _R. J. Mathar_, Sep 17 2008

%p # second Maple program:

%p q:= n-> isprime(n) and isprime(add(1-i, i=Bits[Split](n))):

%p select(q, [$1..500])[]; # _Alois P. Heinz_, Dec 27 2023

%t nmax = 100;

%t Select[Prime[Range[nmax]],

%t PrimeQ[Total@Mod[1 + IntegerDigits[#, 2], 2]] &] (* _Andres Cicuttin_, Jul 08 2020 *)

%t Select[Prime[Range[100]],PrimeQ[DigitCount[#,2,0]]&] (* _Harvey P. Dale_, Feb 03 2021 *)

%o (Python)

%o from sympy import isprime

%o def ok(n): return isprime(n.bit_length()-n.bit_count()) and isprime(n)

%o print([k for k in range(464) if ok(k)]) # _Michael S. Branicky_, Dec 27 2023

%Y Cf. A081092, A144214. Intersection of A000040 and A144754.

%K base,nonn

%O 1,1

%A _Leroy Quet_, Sep 14 2008

%E More terms from _R. J. Mathar_, Sep 17 2008