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Primes in whose binary expansion the number of 1-bits is <= 6 + number of 0-bits.
4

%I #16 Aug 18 2016 12:05:50

%S 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,

%T 97,101,103,107,109,113,131,137,139,149,151,157,163,167,173,179,181,

%U 191,193,197,199,211,223,227,229,233,239,241,251,257,263,269

%N Primes in whose binary expansion the number of 1-bits is <= 6 + number of 0-bits.

%C Differs from primes (A000040) first time at n=31, where a(31)=131, while A000040(31)=127, as 127 whose binary expansion is 1111111, with 7 1-bits and no 0-bits is the first prime excluded from this sequence.

%H Harvey P. Dale, <a href="/A095313/b095313.txt">Table of n, a(n) for n = 1..1000</a>

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

%t Select[Prime[Range[100]],DigitCount[#,2,1]<= DigitCount[#,2,0]+6&] (* _Harvey P. Dale_, Aug 18 2016 *)

%o (PARI)forprime(p=2,269,v=binary(p);s=0;for(k=1,#v,s+=if(v[k]==1,+1,-1));if(s<=6,print1(p,", "))) \\ _Washington Bomfim_, Jan 13 2011

%Y Complement of A095312 in A000040. Subset: A095285, from which it differs first time at n=42, where a(42)=191 (10111111 in binary), while A095285(42)=193 (11000001 in binary). Cf. also A095333.

%K nonn,base,easy

%O 1,1

%A _Antti Karttunen_, Jun 04 2004