A340466 Primes whose binary expansion contains more 1's than 0's but at least one 0.

5, 11, 13, 19, 23, 29, 43, 47, 53, 59, 61, 71, 79, 83, 89, 101, 103, 107, 109, 113, 151, 157, 167, 173, 179, 181, 191, 199, 211, 223, 227, 229, 233, 239, 241, 251, 271, 283, 307, 311, 313, 317, 331, 347, 349, 359, 367, 373, 379, 383, 397, 409, 419, 421, 431

Offset: 1

Author

Ctibor O. Zizka, Jan 08 2021

Keywords

• nonn
• base
• easy

Examples

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

Crossrefs

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

Programs

Mathematica

Select[Range[400], PrimeQ[#] && First[d = DigitCount[#, 2]] > Last[d] > 0 &] (* Amiram Eldar, Jan 08 2021 *)

PARI

isok(n) = if (isprime(n), my(nb=#binary(n), h=hammingweight(n)); (2*h > nb) && (h < nb)); \\ Michel Marcus, Jan 10 2021

Python

from sympy import sieve
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

Formula

{ A095070 } minus { A000225 }.

{ A095070 } minus { A000668 }.

{ A095070 } intersect { A138837 }.