

A143030


A sequence of asymptotic density zeta(4)  1, where zeta is the Riemann zeta function.


2



7, 23, 39, 50, 55, 71, 87, 103, 104, 119, 135, 151, 167, 183, 199, 212, 215, 231, 247, 263, 266, 279, 295, 311, 327, 343, 359, 364, 366, 374, 375, 391, 407, 423, 428, 439, 455, 471, 487, 503, 519, 535, 536, 551, 567, 583, 590, 599, 615, 631, 647, 663, 679
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OFFSET

1,1


COMMENTS

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 (m2)!, Floor[x/(m!)] and Floor[x/(m*(m!))] are congruent to m1 mod m, but Floor[x/((m^2)*(m!))] is not. The sequence is made up of the residue classes 7 mod 16; 50 and 104 mod 162; 364, 366, 748, 750, 1132 and 1134 mod 1536, etc. A set of such sequences with entries for each zeta(k)  1 partitions the integers. See the linked paper for their construction.


LINKS

Table of n, a(n) for n=1..53.
W. J. Keith, Sequences of density zeta(k)  1, arXiv:0905.3765


CROSSREFS

Cf. A143028A143036.
Sequence in context: A098039 A132237 A227064 * A031043 A183126 A213632
Adjacent sequences: A143027 A143028 A143029 * A143031 A143032 A143033


KEYWORD

nonn


AUTHOR

William J. Keith, Jul 18 2008


STATUS

approved



