A340466 - OEIS

%I #26 Jan 11 2021 00:14:18

%S 5,11,13,19,23,29,43,47,53,59,61,71,79,83,89,101,103,107,109,113,151,

%T 157,167,173,179,181,191,199,211,223,227,229,233,239,241,251,271,283,

%U 307,311,313,317,331,347,349,359,367,373,379,383,397,409,419,421,431

%N Primes whose binary expansion contains more 1's than 0's but at least one 0.

%F { A095070 } minus { A000225 }.

%F { A095070 } minus { A000668 }.

%F { A095070 } intersect { A138837 }.

%e 71 is in the sequence because 71 is a prime and 71_10 = 1000111_2. '1000111' has four 1's and three 0's.

%t Select[Range[400], PrimeQ[#] && First[d = DigitCount[#, 2]] > Last[d] > 0 &] (* _Amiram Eldar_, Jan 08 2021 *)

%o (PARI) isok(n) = if (isprime(n), my(nb=#binary(n), h=hammingweight(n)); (2*h > nb) && (h < nb)); \\ _Michel Marcus_, Jan 10 2021

%o (Python)

%o from sympy import sieve

%o A340466_list = [p for p in sieve.primerange(1,10**4) if len(bin(p))-2 < 2*bin(p).count('1') < 2*len(bin(p))-4] # _Chai Wah Wu_, Jan 10 2021

%Y Cf. A000040, A000225, A000668, A066196, A095070, A095071, A138837.

%K nonn,base,easy

%O 1,1

%A _Ctibor O. Zizka_, Jan 08 2021