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Search: id:A027699
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| A027699 |
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Evil primes: primes with even number of 1's in their binary expansion. |
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+0
11
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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Comment from Vladimir Shevelev (shevelev(AT)bgu.ac.il), 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, ...
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
V. Shevelev, A conjecture on primes and a step towards justification
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MATHEMATICA
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Select[Prime[Range[200]], EvenQ[Count[IntegerDigits[ #, 2], 1]]&] - T. D. Noe (noe(AT)sspectra.com), Jun 12 2007
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CROSSREFS
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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: A045416 A038891 A020592 this_sequence A069687 A079017 A100564
Adjacent sequences: A027696 A027697 A027698 this_sequence A027700 A027701 A027702
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KEYWORD
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nonn,easy,base
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AUTHOR
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njas
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EXTENSIONS
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More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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