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 A027699 Evil primes: primes with even number of 1's in their binary expansion. 31
 3, 5, 17, 23, 29, 43, 53, 71, 83, 89, 101, 113, 139, 149, 163, 197, 257, 263, 269, 277, 281, 293, 311, 317, 337, 347, 349, 353, 359, 373, 383, 389, 401, 449, 461, 467, 479, 503, 509, 523, 547, 571, 593, 599, 619, 643, 673, 683, 691, 739, 751, 773, 797, 811 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Comment from Vladimir Shevelev, Jun 01 2007: Conjecture: If pi_1(m) is the number of a(n) not exceeding m and pi_2(m) is the number of A027697(n) not exceeding m then pi_1(m) <= smaller than pi_2(m) for all natural m except m=5 and m=6. I verified this conjecture up to 10^9. Moreover I conjecture that pi_2(m)-pi_1(m) tends to infinity with records at the primes m=2, 13, 41, 61, 67, 79, 109, 131, 137, ... REFERENCES Fouvry, E.; Mauduit, C. 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) LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 MATHEMATICA Select[Prime[Range[200]], EvenQ[Count[IntegerDigits[ #, 2], 1]]&] - T. D. Noe, Jun 12 2007 PROG (PARI) forprime(p=1, 999, norml2(binary(p))%2 || print1(p", ")) (PARI) isA027699(p)=isprime(p) && !bittest(norml2(binary(p)), 0) \\ M. F. Hasler, Dec 12 2010 CROSSREFS Cf. A027697, A066148, A066149. Cf. A001969 (evil numbers), A129771 (evil odd numbers) Cf. A130911 (prime race between evil primes and odious primes). Sequence in context: A218624 A152078 A152079 * A153417 A069687 A079017 Adjacent sequences:  A027696 A027697 A027698 * A027700 A027701 A027702 KEYWORD nonn,easy,base AUTHOR EXTENSIONS More terms from Erich Friedman. STATUS approved

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