A144214 Primes with both a prime number of 0's and a prime number of 1's in their binary representations.

17, 19, 37, 41, 79, 103, 107, 109, 131, 137, 151, 157, 167, 173, 179, 181, 193, 199, 211, 227, 229, 233, 241, 257, 367, 379, 431, 439, 443, 463, 487, 491, 499, 521, 541, 557, 563, 569, 577, 587, 601, 607, 613, 617, 631, 641, 647, 653, 659, 661, 677, 701, 709

Offset: 1

Author

Leroy Quet, Sep 14 2008

Keywords

• base
• nonn

Examples

			79, a prime, in binary is 1001111. This has two 0's and has five 1's. Since both two and five are primes, 79 is included in the sequence.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A081092, A144213, A178350.

Programs

Maple

A080791 := proc(n) local i,dgs ; dgs := convert(n,base,2) ; nops(dgs)-add(i,i=dgs) ; end: A000120 := proc(n) local i,dgs ; dgs := convert(n,base,2) ; add(i,i=dgs) ; end: isA144214 := proc(n) local no0,no1 ; no0 := A080791(n) ; no1 := A000120(n) ; isprime(n) and isprime(no0) and isprime(no1) ; end: for n from 1 to 1200 do if isA144214(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Sep 17 2008

Mathematica

Select[Prime[Range[6! ]],PrimeQ[DigitCount[ #,2,0]]&&PrimeQ[DigitCount[ #,2,1]]&] (* Vladimir Joseph Stephan Orlovsky, Feb 16 2010 *)

Python

from sympy import isprime
def ok(n): return isprime(c:=n.bit_count()) and isprime(n.bit_length()-c) and isprime(n)
print([k for k in range(710) if ok(k)]) # Michael S. Branicky, Dec 27 2023

Extensions

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