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One-bit dominant primes, i.e., primes whose binary expansion contains more 1's than 0's.
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%I #35 Jul 25 2023 04:04:03

%S 3,5,7,11,13,19,23,29,31,43,47,53,59,61,71,79,83,89,101,103,107,109,

%T 113,127,151,157,167,173,179,181,191,199,211,223,227,229,233,239,241,

%U 251,271,283,307,311,313,317,331,347,349,359,367,373,379,383

%N One-bit dominant primes, i.e., primes whose binary expansion contains more 1's than 0's.

%H Indranil Ghosh, <a href="/A095070/b095070.txt">Table of n, a(n) for n = 1..20000</a>

%H Antti Karttunen and John Moyer, <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>.

%H MathOverflow, <a href="https://mathoverflow.net/questions/97288/primes-with-more-ones-than-zeroes-in-their-binary-expansion">Primes with more ones than zeroes in their Binary expansion</a>, 2012.

%e 23 is in the sequence because 23 is a prime and 23_10 = 10111_2. '10111' has four 1's and one 0. - _Indranil Ghosh_, Jan 31 2017

%t Select[Prime[Range[70]], Plus@@IntegerDigits[#, 2] > Length[IntegerDigits[#, 2]]/2 &] (* _Alonso del Arte_, Jan 11 2011 *)

%t Select[Prime[Range[100]], Differences[DigitCount[#, 2]][[1]] < 0 &] (* _Amiram Eldar_, Jul 25 2023 *)

%o (PARI) B(x) = {nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;

%o for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );

%o if(b1 > b0, return(1);, return(0););};

%o forprime(x = 3, 383, if(B(x), print1(x, ", "); ); ); \\ _Washington Bomfim_, Jan 11 2011

%o (PARI) has(n)=hammingweight(n)>#binary(n)/2

%o select(has, primes(500)) \\ _Charles R Greathouse IV_, May 02 2013

%o (Python)

%o # Program to generate the b-file

%o from sympy import isprime

%o i=1

%o j=1

%o while j<=200:

%o if isprime(i) and bin(i)[2:].count("1")>bin(i)[2:].count("0"):

%o print(str(j)+" "+str(i))

%o j+=1

%o i+=1 # _Indranil Ghosh_, Jan 31 2017

%Y Intersection of A000040 and A072600.

%Y Complement of A095075 in A000040.

%Y Subsequence: A095073.

%Y Cf. A095020.

%K nonn,easy,base

%O 1,1

%A _Antti Karttunen_, Jun 01 2004