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

1,1

Links

Table of n, a(n) for n=1..55.

Formula

{ A095070 } minus { A000225 }.

{ A095070 } minus { A000668 }.

{ A095070 } intersect { A138837 }.

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A153418 A079019 A191034 * A222219 A023225 A206581

Adjacent sequences: A340463 A340464 A340465 * A340467 A340468 A340469

Keyword

nonn,base,easy

Author

Ctibor O. Zizka, Jan 08 2021

Status

approved