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Search: id:A143029
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| A143029 |
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A sequence of asymptotic density \zeta(3) - 1, where \zeta is the Riemann zeta function. |
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+0
3
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| 3, 11, 14, 19, 27, 32, 35, 43, 51, 59, 67, 68, 75, 76, 78, 83, 86, 91, 99, 107, 115, 122, 123, 131, 139, 140, 147, 155, 163, 171, 172, 174, 176, 179, 187, 194, 195, 203, 211, 219, 227, 230, 235, 243, 248, 251, 259, 267, 268, 270, 275, 283, 284, 291, 299, 302
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OFFSET
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1,1
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COMMENT
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x is an element of this sequence if when m 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 congruent to m-1 mod m and Floor[x/(m*(m!))] is not congruent to m-1 mod m. The sequence is made up of the residue classes 3 mod 8; 14 and 32 mod 54; 76, 78, 172, 174, 268 and 270 mod 384, etc. A set of such sequences with entries for each \zeta(k) - 1 partitions the integers. See the linked paper for their construction.
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LINKS
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W. J. Keith, Sequences of density \zeta(k) - 1, preprint
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FORMULA
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a(n) = 2*a(n-1) + 3; generating function = 1/(exp(x)-1).
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CROSSREFS
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Cf. A143028-A143036.
Sequence in context: A063963 A101585 A115214 this_sequence A022123 A132363 A134629
Adjacent sequences: A143026 A143027 A143028 this_sequence A143030 A143031 A143032
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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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