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Search: id:A127977
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A127977 Arises in Shevelev's conjecture on evil primes and odious primes. +0
1
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)
OFFSET

1,2

COMMENT

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.

LINKS

Vladimir Shevelev, A Conjecture on Primes and a Step towards Juctification, Jun 06 2007, table 1, p. 2.

FORMULA

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)).

CROSSREFS

Cf. A000040, A000069, A001969, A027697, A027699, A095005, A095006.

Adjacent sequences: A127974 A127975 A127976 this_sequence A127978 A127979 A127980

Sequence in context: A002152 A002466 A109853 this_sequence A112997 A037032 A090752

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post (jvospost2(AT)yahoo.com), Jun 07 2007

page 1

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Last modified May 16 22:57 EDT 2008. Contains 139737 sequences.


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