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%I #28 Jul 20 2022 01:26:36
%S 23,29,43,53,71,83,89,101,113,139,149,163,197,263,269,277,281,293,337,
%T 353,389,401,449,523,547,593,643,673,773,1031,1049,1061,1091,1093,
%U 1097,1217,1283,1289,1297,1409,1553,1601,2069,2083,2089,2129
%N Primes with four 1-bits in their binary expansion.
%H T. D. Noe, <a href="/A095077/b095077.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[320]], Plus@@IntegerDigits[#, 2] == 4 &] (* _Alonso del Arte_, Jan 11 2011 *)
%t Select[ Flatten[ Table[2^i + 2^j + 2^k + 1, {i, 3, 11}, {j, 2, i - 1}, {k, j - 1}]], PrimeQ] (* _Robert G. Wilson v_, Jul 30 2016 *)
%o (PARI) bits1_4(x) = { nB = floor(log(x)/log(2)); z = 0;
%o for(i=0,nB,if(bittest(x,i),z++;if(z>4,return(0););););
%o if(z == 4, return(1);, return(0););};
%o forprime(x=17,2129,if(bits1_4(x),print1(x, ", ");););
%o \\ _Washington Bomfim_, Jan 11 2011
%o (PARI) is(n)=isprime(n) && hammingweight(n)==4 \\ _Charles R Greathouse IV_, Jul 30 2016
%o (PARI) list(lim)=my(v=List(),t); for(a=3,logint(lim\=1,2), for(b=2,a-1, for(c=1,b-1, t=1<<a + 1<<b + 1<<c + 1; if(t>lim, return(Vec(v))); if(isprime(t), listput(v,t))))); Vec(v) \\ _Charles R Greathouse IV_, Jul 30 2016
%o (Python)
%o from itertools import count, islice
%o from sympy import isprime
%o from sympy.utilities.iterables import multiset_permutations
%o def A095077_gen(): # generator of terms
%o return filter(isprime,map(lambda s:int('1'+''.join(s)+'1',2),(s for l in count(2) for s in multiset_permutations('0'*(l-2)+'11'))))
%o A095077_list = list(islice(A095077_gen(),30)) # _Chai Wah Wu_, Jul 19 2022
%Y Subsequence of A027699. First differs from A085448 at n = 19, where a(n)=337, while A085448 continues from there with 311, whose binary expansion has six 1-bits, not four. Cf. A095057.
%Y Cf. A000215 (primes having two bits set), A081091 (three bits set).
%Y Cf. A264908.
%K nonn,easy,base
%O 1,1
%A _Antti Karttunen_, Jun 01 2004
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