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A143033
A sequence of asymptotic density zeta(7) - 1, where zeta is the Riemann zeta function.
10
63, 191, 319, 447, 575, 703, 831, 959, 1087, 1215, 1343, 1454, 1471, 1599, 1727, 1855, 1983, 2111, 2239, 2367, 2495, 2623, 2751, 2879, 2912, 3007, 3135, 3263, 3391, 3519, 3647, 3775, 3903, 4031, 4159, 4287, 4415, 4543, 4671, 4799, 4927, 5055, 5183, 5311
OFFSET
1,1
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
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.
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[5300], f[#] == 7 &] (* Amiram Eldar, Feb 15 2021 after Kevin Ryde at A161189 *)
KEYWORD
nonn
AUTHOR
William J. Keith, Jul 18 2008
STATUS
approved