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A143034 A sequence of asymptotic density zeta(8) - 1, where zeta is the Riemann zeta function. 10

%I

%S 127,383,639,895,1151,1407,1663,1919,2175,2431,2687,2943,3199,3455,

%T 3711,3967,4223,4370,4479,4735,4991,5247,5503,5759,6015,6271,6527,

%U 6783,7039,7295,7551,7807,8063,8319,8575,8744,8831,9087,9343,9599,9855,10111

%N A sequence of asymptotic density zeta(8) - 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="/A143034/b143034.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[10^4], f[#] == 8 &] (* _Amiram Eldar_, Feb 15 2021 after _Kevin Ryde_ at A161189 *)

%Y Cf. A143028, A143029, A143030, A143031, A143032, A143033, A143035, A143036, A161189, A339013.

%K nonn

%O 1,1

%A _William J. Keith_, Jul 18 2008

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Last modified June 14 15:19 EDT 2021. Contains 345025 sequences. (Running on oeis4.)