cp's OEIS Frontend

A095315 Primes in whose binary expansion the number of 1 bits is <= 2 + number of 0 bits.

%I A095315 #27 Apr 28 2025 12:20:50
%S A095315 2,3,5,11,13,17,19,37,41,43,53,67,71,73,83,89,97,101,113,131,137,139,
%T A095315 149,151,157,163,167,173,179,181,193,197,199,211,227,229,233,241,257,
%U A095315 263,269,271,277,281,283,293,307,313,331,337,353,389,397
%N A095315 Primes in whose binary expansion the number of 1 bits is <= 2 + number of 0 bits.
%H A095315 Indranil Ghosh, <a href="/A095315/b095315.txt">Table of n, a(n) for n = 1..25000</a> (terms 1..1000 from Harvey P. Dale)
%H A095315 Antti Karttunen and J. Moyer, <a href="/A095062/a095062.c.txt">C program for computing the initial terms of this sequence</a>
%e A095315 13 is in the sequence because 13 = 1101_2. '1101' has three 1's and one 0. 3 = 2 + 1. - _Indranil Ghosh_, Feb 07 2017
%t A095315 Select[Prime[Range[100]],DigitCount[#,2,1]<3+DigitCount[#,2,0]&] (* _Harvey P. Dale_, Aug 12 2016 *)
%o A095315 (PARI) B(x) = { nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;
%o A095315 for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );
%o A095315 if(b1 <= (2+b0), return(1);, return(0););};
%o A095315 forprime(x = 2, 397, if(B(x), print1(x, ", "); ); );
%o A095315 \\ _Washington Bomfim_, Jan 12 2011
%o A095315 (Python)
%o A095315 from sympy import isprime
%o A095315 i=j=1
%o A095315 while j<=250:
%o A095315     if isprime(i) and bin(i)[2:].count("1")<=2+bin(i)[2:].count("0"):
%o A095315         print(str(j)+" "+str(i))
%o A095315         j+=1
%o A095315     i+=1 # _Indranil Ghosh_, Feb 07 2017
%Y A095315 Complement of A095314 in A000040. Subset: A095287. Subset of A095319. Cf. also A095335.
%K A095315 nonn,easy
%O A095315 1,1
%A A095315 _Antti Karttunen_, Jun 04 2004