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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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21
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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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Comment from Vladimir Shevelev: Conjecture: a(n) < A027699(n) except for n = 2. I verified this conjecture up to n=5*10^7. Moreover, I conjecture that A027699(n) - a(n) tends to infinity.
Item 2 of Green is about this sequence: "This is an expository article to accompany my two lectures at the CDM conference. I have used this an excuse to make public two sets of notes I had lying around and also to put together a short reader's guide to some recent joint work with T. Tao. Contents: 1. An exposition, without much detail, of the work of Goldston, Pintz and Yildirim on gaps between primes; 2. A detailed discussion of the work of Mauduit and Rivat establishing that 50 percent of the primes have odd digit sum when written in base 2; 3. A reader's guide to recent work of T. Tao and the author on linear equations in primes. The sections can be read independently." - Jonathan Vos Post, Oct 04 2007
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
Ben Green, Three topics in additive prime number theory, Oct 03, 2007, pp. 12-27.
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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 [From Vladimir Joseph Stephan Orlovsky, Apr 06 2009]
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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)};
forprime(p=2, 563, if(f(p), print1(p, ", "))) - [W. Bomfim webonfim(AT)bol.com Jan 14, 2011]
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CROSSREFS
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Cf. A027699, A066148, A066149.
Cf. A000069 (odious numbers), A092246 (odd odious numbers)
Sequence in context: A161681 A020583 A140557 * A146315 A038892 A019346
Adjacent sequences: A027694 A027695 A027696 * A027698 A027699 A027700
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KEYWORD
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nonn,easy,base
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AUTHOR
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N. J. A. Sloane.
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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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