A143032 A sequence of asymptotic density zeta(6) - 1, where zeta is the Riemann zeta function.

31, 95, 159, 223, 287, 351, 415, 479, 482, 543, 607, 671, 735, 799, 863, 927, 968, 991, 1055, 1119, 1183, 1247, 1311, 1375, 1439, 1503, 1567, 1631, 1695, 1759, 1823, 1887, 1940, 1951, 2015, 2079, 2143, 2207, 2271, 2335, 2399, 2426, 2463, 2527, 2591, 2655

Offset: 1

Author

William J. Keith, Jul 18 2008

Keywords

• nonn

Comments

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.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• William J. Keith, Sequences of Density zeta(K) - 1, INTEGERS, Vol. 10 (2010), Article #A19, pp. 233-241. Also arXiv preprint, arXiv:0905.3765 [math.NT], 2009 and author's copy.

Crossrefs

Cf. A143028, A143029, A143030, A143031, A143033, A143034, A143035, A143036, A161189, A339013.

Programs

Mathematica

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[2700], f[#] == 6 &] (* Amiram Eldar, Feb 15 2021 after Kevin Ryde at A161189 *)