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 A027697 Odious primes: primes with odd number of 1's in binary expansion. 39
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS T. D. Noe, Table of n, a(n) for n=1..10000 E. Fouvry, C. Mauduit, Sommes des chiffres et nombres presque premiers, (French) [Sums of digits and almost primes] Math. Ann. 305 (1996), no. 3, 571--599. MR1397437 (97k:11029) Ben Green, Three topics in additive prime number theory, arXiv:0710.0823 [math.NT], Oct 03, 2007, pp. 12-27. V. Shevelev, Generalized Newman phenomena and digit conjectures on primes, Internat. J. of Mathematics and Math. Sciences, 2008 (2008), Article ID 908045, 1-12. MAPLE 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 MATHEMATICA 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 *) PROG (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, ", "))) \\ Washington Bomfim, Jan 14 2011 (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 CROSSREFS Cf. A027699, A066148, A066149. Cf. A000069 (odious numbers), A092246 (odd odious numbers) Sequence in context: A161681 A020583 A140557 * A235475 A146315 A038892 Adjacent sequences:  A027694 A027695 A027696 * A027698 A027699 A027700 KEYWORD nonn,easy,base AUTHOR EXTENSIONS More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu) STATUS approved

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Last modified April 21 04:42 EDT 2021. Contains 343146 sequences. (Running on oeis4.)