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A095071 Zero-bit dominant primes, i.e., primes whose binary expansion contains more 0's than 1's.

%I A095071 #27 Nov 28 2024 16:31:23
%S A095071 17,67,73,97,131,137,193,257,263,269,277,281,293,337,353,389,401,449,
%T A095071 521,523,547,577,593,641,643,673,769,773,1031,1033,1039,1049,1051,
%U A095071 1061,1063,1069,1091,1093,1097,1109,1123,1129,1153,1163,1171
%N A095071 Zero-bit dominant primes, i.e., primes whose binary expansion contains more 0's than 1's.
%H A095071 Indranil Ghosh, <a href="/A095071/b095071.txt">Table of n, a(n) for n = 1..20000</a>
%H A095071 A. Karttunen and J. Moyer, <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>
%e A095071 73 is in the sequence because 73 is a prime and 73_10 = 1001001_2. '1001001' has four 0's and one 1. - _Indranil Ghosh_, Jan 31 2017
%t A095071 Reap[Do[p=Prime[k];id=IntegerDigits[p,2];n=Length@id;If[Count[id,0]>n/2,Sow[p]],{k,200}]][[2,1]]
%t A095071 (* _Zak Seidov_ *)
%t A095071 Select[Prime[Range[200]],DigitCount[#,2,0]>DigitCount[#,2,1]&] (* _Harvey P. Dale_, Nov 28 2024 *)
%o A095071 (PARI) B(x) = { nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;
%o A095071 for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );
%o A095071 if(b0 > b1, return(1);, return(0););};
%o A095071 forprime(x = 2, 1171, if(B(x), print1(x, ", "); ); ); \\ _Washington Bomfim_, Jan 11 2011
%o A095071 (PARI){forprime(p=2,1171,nB=floor(log(p)/log(2));
%o A095071 sum(i=0,nB,bittest(p,i))<=nB/2&print1(p,","))} \\ _Zak Seidov_, Jan 11 2011
%o A095071 (Python)
%o A095071 #Program to generate the b-file
%o A095071 from sympy import isprime
%o A095071 i=1
%o A095071 j=1
%o A095071 while j<=200:
%o A095071     if isprime(i) and bin(i)[2:].count("0")>bin(i)[2:].count("1"):
%o A095071         print(str(j)+" "+str(i))
%o A095071         j+=1
%o A095071     i+=1 # _Indranil Ghosh_, Jan 31 2017
%Y A095071 Complement of A095074 in A000040. Subset: A095072. Cf. A095019.
%K A095071 nonn,base,easy
%O A095071 1,1
%A A095071 _Antti Karttunen_, Jun 01 2004