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A095075 Primes in whose binary expansion the number of 1-bits is less than or equal to number of 0-bits. 6

%I #30 Sep 27 2023 16:50:40

%S 2,17,37,41,67,73,97,131,137,139,149,163,193,197,257,263,269,277,281,

%T 293,337,353,389,401,449,521,523,541,547,557,563,569,577,587,593,601,

%U 613,617,641,643,647,653,659,661,673,677,709,769,773,787

%N Primes in whose binary expansion the number of 1-bits is less than or equal to number of 0-bits.

%H Indranil Ghosh, <a href="/A095075/b095075.txt">Table of n, a(n) for n = 1..25000</a>

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

%e From _Indranil Ghosh_, Feb 03 2017: (Start)

%e 17 is in the sequence because 17_10 = 10001_2. '10001' has two 1's and three 0's.

%e 37 is in the sequence because 37_10 = 100101_2. '100101' has three 1's and 3 0's. (End)

%t Select[Prime[Range[150]], Differences[DigitCount[#, 2]][[1]] >= 0 &] (* _Amiram Eldar_, Jul 25 2023 *)

%t Select[Prime[Range[150]],DigitCount[#,2,1]<=DigitCount[#,2,0]&] (* _Harvey P. Dale_, Sep 27 2023 *)

%o (PARI) B(x) = {nB = floor(log(x)/log(2)); z1 = 0; z0 = 0;

%o for(i = 0, nB, if(bittest(x,i), z1++;, z0++;); );

%o if(z1 <= z0, return(1);, return(0););};

%o forprime(x = 2, 787, if(B(x), print1(x, ", "); ); );

%o \\ _Washington Bomfim_, Jan 11 2011

%o (Python)

%o from sympy import isprime

%o i=1

%o j=1

%o while j<=250:

%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_, Feb 03 2017

%Y Complement of A095070 in A000040.

%Y Cf. A095055.

%K nonn,easy,base

%O 1,1

%A _Antti Karttunen_, Jun 01 2004

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)