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Primes with an odd number of 0's in binary expansion.
5

%I #36 Apr 17 2020 10:37:45

%S 2,5,11,13,17,23,29,37,41,47,59,61,71,83,89,101,113,131,137,151,157,

%T 167,173,179,181,191,193,199,211,223,227,229,233,239,241,251,257,263,

%U 269,277,281,293,311,317,337,347,349,353,359,373,383,389,401,449,461

%N Primes with an odd number of 0's in binary expansion.

%H Indranil Ghosh, <a href="/A066149/b066149.txt">Table of n, a(n) for n = 1..20000</a> (terms 1..1000 from T. D. Noe)

%e 17 is in the sequence because 17 is a prime and 17 = 10001_2. '10001' has three 0's. - _Indranil Ghosh_, Feb 06 2017

%t Select[ Prime[ Range[ PrimePi[ 1000 ] ] ], OddQ[ Count[ IntegerDigits[ #, 2 ], 0 ] ]& ]

%o (PARI) forprime(p=2, 10^3, if( #select(x->x==0, digits(p, 2))%2==1, print1(p, ", "))); \\ _Joerg Arndt_, Jun 16 2018

%Y Cf. A066148, A027699, A027697.

%Y Cf. A059009.

%K nonn,easy,base

%O 1,1

%A _R. K. Guy_, Dec 13 2001

%E More terms from _Vladeta Jovovic_ and _Klaus Brockhaus_, Dec 13 2001