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Search: id:A127977
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| A127977 |
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Arises in Shevelev's conjecture on evil primes and odious primes. |
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1
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| 0, 2, 4, 7, 13, 19, 39, 54, 104, 139, 251, 334, 590, 716, 1353, 1855, 3659, 5221, 10484, 14933, 27491, 35474, 68816, 97342, 186405, 265255
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Shevelev conjectures (p.2) that for all natural numbers n other than 5 and 6, the number of evil primes not exceeding n <= the number of odious primes not exceeding n. Odious primes are A000040 INTERSECTION A000069. Evil primes are A000040 INTERSECTION A001969. A000069 Odious numbers: odd number of 1's in binary expansion. A001969 Evil numbers: even number of 1's in binary expansion.
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LINKS
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Vladimir Shevelev, A Conjecture on Primes and a Step towards Justification, Jun 06 2007, table 1, p. 2, arXiv:0706.0786
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FORMULA
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a(n) = MIN[k in (2^(n-1),2^n)] ((the number of odious primes not exceeding k) - the number of evil primes not exceeding k)). a(n) = MIN[k in (2^(n-1),2^n)] (A027697(k) - A027699(k)).
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CROSSREFS
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Cf. A000040, A000069, A001969, A027697, A027699, A095005, A095006.
Sequence in context: A162842 A164901 A109853 this_sequence A112997 A037032 A165753
Adjacent sequences: A127974 A127975 A127976 this_sequence A127978 A127979 A127980
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KEYWORD
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easy,nonn,new
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 07 2007
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EXTENSIONS
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Replaced arXiv URL by non-cached version - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 30 2009
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