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A027697
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Odious primes: primes with odd number of 1's in binary expansion.
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42
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2, 7, 11, 13, 19, 31, 37, 41, 47, 59, 61, 67, 73, 79, 97, 103, 107, 109, 127, 131, 137, 151, 157, 167, 173, 179, 181, 191, 193, 199, 211, 223, 227, 229, 233, 239, 241, 251, 271, 283, 307, 313, 331, 367, 379, 397, 409, 419, 421, 431, 433, 439, 443, 457, 463, 487, 491, 499, 521, 541, 557, 563
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OFFSET
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1,1
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COMMENTS
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Conjecture: a(n) < A027699(n) except for n = 2; verified up to n=5*10^7. Moreover, I conjecture that A027699(n) - a(n) tends to infinity. - Vladimir Shevelev
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LINKS
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MAPLE
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a:=proc(n) local nn: nn:= convert(ithprime(n), base, 2): if `mod`(sum(nn[j], j =1..nops(nn)), 2)=1 then ithprime(n) else end if end proc: seq(a(n), n=1..103); # Emeric Deutsch, Oct 24 2007
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MATHEMATICA
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Clear[BinSumOddQ]; BinSumOddQ[a_]:=Module[{i, s=0}, s=0; For[i=1, i<=Length[IntegerDigits[a, 2]], s+=Extract[IntegerDigits[a, 2], i]; i++ ]; OddQ[s]]; lst={}; Do[p=Prime[n]; If[BinSumOddQ[p], AppendTo[lst, p]], {n, 4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 06 2009 *)
Select[Prime@ Range@ 120, OddQ@ First@ DigitCount[#, 2] &] (* Michael De Vlieger, Feb 08 2016 *)
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PROG
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(PARI) f(p)={v=binary(p); s=0; for(k=1, #v, if(v[k]==1, s++)); return(s%2)};
(PARI) s=[]; forprime(p=2, 1000, if(norml2(binary(p))%2==1, s=concat(s, p))); s \\ Colin Barker, Feb 18 2014
(Python)
from sympy import primerange
print([n for n in primerange(1, 1001) if bin(n)[2:].count("1")%2]) # Indranil Ghosh, May 03 2017
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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EXTENSIONS
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More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)
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STATUS
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approved
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