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Search: id:A143028
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| A143028 |
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A sequence of asymptotic density \zeta(2) - 1, where \zeta is the Riemann zeta function. |
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+0
10
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| 1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 16, 17, 18, 20, 21, 22, 24, 25, 26, 28, 29, 30, 33, 34, 36, 37, 38, 40, 41, 42, 44, 45, 46, 48, 49, 52, 53, 54, 56, 57, 58, 60, 61, 62, 64, 65, 66, 69, 70, 72, 73, 74, 77, 80, 81, 82, 84, 85, 88, 89, 90, 92, 93, 94, 96, 97, 98, 100, 101, 102, 105
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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x is an element of this sequence if when m>1 is the least natural number such that the least positive residue of x mod m! is no more than (m-2)!, Floor[x/(m!)] is not congruent to m-1 mod m. The sequence is made up of the residue classes 1 mod 4; 2 and 8 mod 18; 4, 6, 28, 30, 52 and 54 mod 96, etc. A set of such sequences with entries for each \zeta(k) - 1 partitions the integers. See the linked paper for their construction.
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 07 2009: (Start)
A161189(n) = 2 if n = a term in A143028. Similarly A161189(n) = 3, 4,
5,...if n is in A143029, A143030...; such that the number system is
partitioned into relative densities tending to (Zeta(2) - 1), (Zeta(3) - 1),...
such that Sum_{k=2..inf.}: (Zeta(k) - 1) = 1.0. This implies that the density
of 2's in A161189 tends to (Zeta(2) - 1) = (Pi^2/6 - 1) = .644934... (End)
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LINKS
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W. J. Keith, Sequences of density \zeta(k) - 1, preprint
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CROSSREFS
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Cf. A143029-A143036.
A161189 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 07 2009]
Sequence in context: A003511 A059567 A006594 this_sequence A091529 A095775 A035063
Adjacent sequences: A143025 A143026 A143027 this_sequence A143029 A143030 A143031
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KEYWORD
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nonn
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AUTHOR
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William J. Keith (wjk26(AT)drexel.edu), Jul 17 2008, Jul 18 2008
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