A095077 Primes with four 1-bits in their binary expansion.
23, 29, 43, 53, 71, 83, 89, 101, 113, 139, 149, 163, 197, 263, 269, 277, 281, 293, 337, 353, 389, 401, 449, 523, 547, 593, 643, 673, 773, 1031, 1049, 1061, 1091, 1093, 1097, 1217, 1283, 1289, 1297, 1409, 1553, 1601, 2069, 2083, 2089, 2129
Offset: 1
Links
- T. D. Noe, Table of n, a(n) for n = 1..1000
- A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence
Crossrefs
Programs
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Mathematica
Select[Prime[Range[320]], Plus@@IntegerDigits[#, 2] == 4 &] (* Alonso del Arte, Jan 11 2011 *) 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 *)
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PARI
bits1_4(x) = { nB = floor(log(x)/log(2)); z = 0; for(i=0,nB,if(bittest(x,i),z++;if(z>4,return(0);););); if(z == 4, return(1);, return(0););}; forprime(x=17,2129,if(bits1_4(x),print1(x, ", "););); \\ Washington Bomfim, Jan 11 2011 -
PARI
is(n)=isprime(n) && hammingweight(n)==4 \\ Charles R Greathouse IV, Jul 30 2016
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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<lim, return(Vec(v))); if(isprime(t), listput(v,t))))); Vec(v) \\ Charles R Greathouse IV, Jul 30 2016
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Python
from itertools import count, islice from sympy import isprime from sympy.utilities.iterables import multiset_permutations def A095077_gen(): # generator of terms 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')))) A095077_list = list(islice(A095077_gen(),30)) # Chai Wah Wu, Jul 19 2022
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