cp's OEIS Frontend

A095323 Primes in whose binary expansion the number of 1 bits is <= 4 + number of 0 bits.

%I A095323 #14 Dec 09 2015 08:27:43
%S A095323 2,3,5,7,11,13,17,19,23,29,37,41,43,47,53,59,61,67,71,73,79,83,89,97,
%T A095323 101,103,107,109,113,131,137,139,149,151,157,163,167,173,179,181,193,
%U A095323 197,199,211,227,229,233,241,257,263,269,271,277,281,283,293
%N A095323 Primes in whose binary expansion the number of 1 bits is <= 4 + number of 0 bits.
%C A095323 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 five 1 bits and no 0 bits is the first prime excluded from this sequence. Note that 15 (1111 in binary) is not prime.
%H A095323 A. Karttunen and J. Moyer: <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>
%t A095323 Select[Prime[Range[100]],DigitCount[#,2,1]<(5+DigitCount[#,2,0])&] (* _Harvey P. Dale_, Dec 09 2015 *)
%o A095323 (PARI) B(x) = { nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;
%o A095323 for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );
%o A095323 if(b1 <= (4+b0), return(1);, return(0););};
%o A095323 forprime(x = 2, 293, if(B(x), print1(x, ", "); ); ); \\ _Washington Bomfim_, Jan 12 2011
%Y A095323 Complement of A095322 in A000040. Subset of A095285. subset: A095319. Cf. A095325.
%K A095323 nonn,base,easy
%O A095323 1,1
%A A095323 _Antti Karttunen_, Jun 04 2004