cp's OEIS Frontend

A095319 Primes in whose binary expansion the number of 1 bits is <= 3 + number of 0 bits.

%I A095319 #15 Feb 22 2020 20:10:39
%S A095319 2,3,5,7,11,13,17,19,23,29,37,41,43,53,67,71,73,79,83,89,97,101,103,
%T A095319 107,109,113,131,137,139,149,151,157,163,167,173,179,181,193,197,199,
%U A095319 211,227,229,233,241,257,263,269,271,277,281,283,293,307,311
%N A095319 Primes in whose binary expansion the number of 1 bits is <= 3 + number of 0 bits.
%C A095319 Differs from primes (A000040) first time at n=11, where a(11)=37, while A000040(11)=31, as 31 whose binary expansion is 11111, with 5 1-bits and no 0 bits is the first prime excluded from this sequence. - Jun 04 2004
%H A095319 A. Karttunen and J. Moyer: <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>
%t A095319 Select[Prime[Range[70]],DigitCount[#,2,1]<DigitCount[#,2,0]+4&] (* _Harvey P. Dale_, Feb 22 2020 *)
%o A095319 (PARI) B(x) = { nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;
%o A095319 for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );
%o A095319 if(b1 <= (3+b0), return(1);, return(0););};
%o A095319 forprime(x = 2, 311, if(B(x), print1(x, ", "); ); );
%o A095319 \\ _Washington Bomfim_, Jan 12 2011
%Y A095319 Complement of A095318 in A000040. Subset of A095323, subset: A095315. A095329.
%K A095319 nonn,base,easy
%O A095319 1,1
%A A095319 _Antti Karttunen_