A281014 Numbers with both prime number of 0's and prime number of 1's in their binary reflected Gray code representation.

8, 12, 14, 16, 17, 19, 23, 24, 25, 27, 28, 29, 30, 33, 35, 39, 47, 49, 51, 55, 57, 59, 61, 64, 69, 73, 75, 77, 81, 83, 87, 89, 91, 93, 96, 101, 105, 107, 109, 112, 117, 120, 124, 126, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147

Offset: 1

Author

Indranil Ghosh, Jan 13 2017

Keywords

• nonn
• base
• easy

Comments

This sequence is the intersection of A280998 and A280999.

Examples

			27 is in the sequence as it is present in both the sequences A280998 and A280999.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..10000
• Wikipedia, Gray code.

Crossrefs

Cf. A014550, A280998, A280999.

Programs

Mathematica

Select[Range[150], And @@ PrimeQ[DigitCount[BitXor[#, Floor[#/2]], 2]] &] (* Amiram Eldar, May 01 2021 *)

PARI

is(n)=isprime(logint(n,2)-hammingweight(bitxor(n, n>>1))+1) && isprime(hammingweight(bitxor(n, n>>1))) \\ Charles R Greathouse IV, Jan 13 2017