A144213 Primes with a prime number of 0's in their binary representations.

17, 19, 37, 41, 43, 53, 71, 79, 83, 89, 101, 103, 107, 109, 113, 131, 137, 151, 157, 167, 173, 179, 181, 193, 199, 211, 227, 229, 233, 241, 257, 263, 269, 277, 281, 293, 311, 317, 337, 347, 349, 353, 359, 367, 373, 379, 389, 401, 431, 439, 443, 449, 461, 463

Offset: 1

Author

Leroy Quet, Sep 14 2008

Keywords

• base
• nonn

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Maple

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
# second Maple program:
q:= n-> isprime(n) and isprime(add(1-i, i=Bits[Split](n))):
select(q, [$1..500])[];  # Alois P. Heinz, Dec 27 2023

Mathematica

nmax = 100;
Select[Prime[Range[nmax]],
PrimeQ[Total@Mod[1 + IntegerDigits[#, 2], 2]] &] (* Andres Cicuttin, Jul 08 2020 *)
Select[Prime[Range[100]],PrimeQ[DigitCount[#,2,0]]&] (* Harvey P. Dale, Feb 03 2021 *)

Python

from sympy import isprime
def ok(n): return isprime(n.bit_length()-n.bit_count()) and isprime(n)
print([k for k in range(464) if ok(k)]) # Michael S. Branicky, Dec 27 2023

Extensions

More terms from R. J. Mathar, Sep 17 2008