A280872 Primes that have exactly 7 zeros and 7 ones in their binary expansion.

8287, 8311, 8317, 8423, 8429, 8527, 8539, 8563, 8599, 8627, 8629, 8647, 8677, 8681, 8689, 8783, 8807, 8819, 8821, 8861, 8933, 8999, 9011, 9013, 9043, 9049, 9059, 9109, 9137, 9157, 9161, 9277, 9319, 9323, 9337, 9371, 9397, 9419, 9421, 9433, 9511, 9547, 9613, 9619

Offset

1,1

Links

K. D. Bajpai, Table of n, a(n) for n = 1..189

Example

8287 is in the sequence because it is a prime and its binary expansion 10000001011111 contains exactly 7 zeros and 7 ones.
9161 is in the sequence because it is a prime and its binary expansion 10001111001001 contains exactly 7 zeros and 7 ones.

Maple

select(t -> isprime(t) and convert(convert(t, base, 2), `+`)=7, [seq(i, i=2^13+1..2^14-1, 2)]); # Robert Israel, Jan 09 2017

Mathematica

Select[Prime[Range[50000]], Count[IntegerDigits[#, 2], 0] == Count[IntegerDigits[#, 2], 1] == 7 &]
Select[FromDigits[#, 2]&/@(Join[{1}, #]&/@Permutations[ {1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0}]), PrimeQ]//Union (* Harvey P. Dale, May 10 2019 *)

Crossrefs

Cf. A000040, A007088, A014311, A066196.

Sequence in context: A054215 A031589 A031769 * A329342 A237948 A362578

Adjacent sequences: A280869 A280870 A280871 * A280873 A280874 A280875

Keyword

nonn,base,fini,full

Author

K. D. Bajpai, Jan 09 2017

Status

approved