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A143036 A sequence of asymptotic density zeta(10) - 1, where zeta is the Riemann zeta function. 10

%I

%S 511,1535,2559,3583,4607,5631,6655,7679,8703,9727,10751,11775,12799,

%T 13823,14847,15871,16895,17919,18943,19967,20991,22015,23039,24063,

%U 25087,26111,27135,28159,29183,30207,31231,32255,33279,34303,35327

%N A sequence of asymptotic density zeta(10) - 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="/A143036/b143036.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[4*10^4], f[#] == 10 &] (* _Amiram Eldar_, Feb 15 2021 after _Kevin Ryde_ at A161189 *)

%Y Cf. A143028, A143029, A143030, A143031, A143032, A143033, A143034, A143035, A161189, A339013.

%K nonn

%O 1,1

%A _William J. Keith_, Jul 18 2008

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Last modified June 22 20:16 EDT 2021. Contains 345388 sequences. (Running on oeis4.)