A280999 Numbers with a prime number of 0's in their binary reflected Gray code representation.

7, 8, 12, 14, 15, 16, 17, 19, 23, 24, 25, 27, 28, 29, 30, 33, 34, 35, 36, 38, 39, 40, 44, 46, 47, 49, 50, 51, 52, 54, 55, 57, 58, 59, 61, 63, 64, 66, 68, 69, 70, 72, 73, 75, 76, 77, 78, 80, 81, 83, 87, 88, 89, 91, 92, 93, 94, 96, 98, 100, 101, 102, 104, 105, 107

Offset: 1

Author

Indranil Ghosh, Jan 12 2017

Keywords

• nonn
• base
• easy

Examples

			27 is in the sequence because the binary reflected Gray Code representation of 27 is 10110 which has 2 0's and 2 is prime.
		

Links

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

Crossrefs

Cf. A014550, A144754, A280998.

Programs

Mathematica

Select[Range[100], PrimeQ[DigitCount[BitXor[#, Floor[#/2]], 2, 0]] &] (* Amiram Eldar, May 01 2021 *)

PARI

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