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%I #7 Feb 15 2021 02:33:21
%S 255,767,1279,1791,2303,2815,3327,3839,4351,4863,5375,5887,6399,6911,
%T 7423,7935,8447,8959,9471,9983,10495,11007,11519,12031,12543,13055,
%U 13118,13567,14079,14591,15103,15615,16127,16639,17151,17663,18175
%N A sequence of asymptotic density zeta(9) - 1, where zeta is the Riemann zeta function.
%C Made up of a collection of mutually exclusive residue classes modulo multiples of factorials. A set of such sequences with entries for each zeta(k) - 1 partitions the integers. See the linked paper for their construction.
%H Amiram Eldar, <a href="/A143035/b143035.txt">Table of n, a(n) for n = 1..10000</a>
%H William J. Keith, <a href="https://www.emis.de/journals/INTEGERS/papers/k19/k19.Abstract.html">Sequences of Density zeta(K) - 1</a>, INTEGERS, Vol. 10 (2010), Article #A19, pp. 233-241. Also <a href="http://arxiv.org/abs/0905.3765">arXiv preprint</a>, arXiv:0905.3765 [math.NT], 2009 and <a href="http://www.math.drexel.edu/~keith/ZetaKMinusOne.pdf">author's copy</a>.
%t f[n_] := Module[{k = n - 1, m = 2, r}, While[{k, r} = QuotientRemainder[k, m]; r != 0, m++]; IntegerExponent[k + 1, m] + 2]; Select[Range[2*10^4], f[#] == 9 &] (* _Amiram Eldar_, Feb 15 2021 after _Kevin Ryde_ at A161189 *)
%Y Cf. A143028, A143029, A143030, A143031, A143032, A143033, A143034, A143036, A161189, A339013.
%K nonn
%O 1,1
%A _William J. Keith_, Jul 18 2008
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