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A095077
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Primes with four 1-bits in their binary expansion.
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5
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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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
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MATHEMATICA
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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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PROG
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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
(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
(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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CROSSREFS
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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.
Cf. A000215 (primes having two bits set), A081091 (three bits set).
Cf. A264908.
Sequence in context: A007637 A161723 A085448 * A106989 A106988 A127834
Adjacent sequences: A095074 A095075 A095076 * A095078 A095079 A095080
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KEYWORD
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nonn,easy,base
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AUTHOR
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Antti Karttunen, Jun 01 2004
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STATUS
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approved
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