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

%I #19 May 01 2021 07:32:55

%S 8,12,14,16,17,19,23,24,25,27,28,29,30,33,35,39,47,49,51,55,57,59,61,

%T 64,69,73,75,77,81,83,87,89,91,93,96,101,105,107,109,112,117,120,124,

%U 126,129,131,133,135,137,139,141,143,145,147

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

%C This sequence is the intersection of A280998 and A280999.

%H Indranil Ghosh, <a href="/A281014/b281014.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Gray_code">Gray code</a>.

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

%t Select[Range[150], And @@ PrimeQ[DigitCount[BitXor[#, Floor[#/2]], 2]] &] (* _Amiram Eldar_, May 01 2021 *)

%o (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

%Y Cf. A014550, A280998, A280999.

%K nonn,base,easy

%O 1,1

%A _Indranil Ghosh_, Jan 13 2017