A095315 - OEIS

%I #24 May 01 2021 02:10:10

%S 2,3,5,11,13,17,19,37,41,43,53,67,71,73,83,89,97,101,113,131,137,139,

%T 149,151,157,163,167,173,179,181,193,197,199,211,227,229,233,241,257,

%U 263,269,271,277,281,283,293,307,313,331,337,353,389,397

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

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

%e 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 Select[Prime[Range[100]],DigitCount[#,2,1]<3+DigitCount[#,2,0]&] (* _Harvey P. Dale_, Aug 12 2016 *)

%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 <= (2+b0), return(1);, return(0););};

%o forprime(x = 2, 397, if(B(x), print1(x, ", "); ); );

%o \\ _Washington Bomfim_, Jan 12 2011

%o (Python)

%o i=j=1

%o while j<=250:

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

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

%o         j+=1

%o     i+=1 # _Indranil Ghosh_, Feb 07 2017

%Y Complement of A095314 in A000040. Subset: A095287. Subset of A095319. Cf. also A095335.

%K nonn,easy

%O 1,1

%A _Antti Karttunen_, Jun 04 2004