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

Author

K. D. Bajpai, Jan 09 2017

Keywords

• nonn
• base
• fini
• full

Examples

			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.
		

Links

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

Crossrefs

Cf. A000040, A007088, A014311, A066196.

Programs

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 *)