OFFSET
1,1
COMMENTS
x is an element of this sequence if when m is the least natural number such that the least positive residue of x mod m! is no more than (m-2)!, floor(x/(m!)) is congruent to m-1 mod m and floor(x/(m*(m!))) is not congruent to m-1 mod m. The sequence is made up of the residue classes 3 mod 8; 14 and 32 mod 54; 76, 78, 172, 174, 268 and 270 mod 384, etc. 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.
FORMULA
a(n) = 2*a(n-1) + 3. [Obviously wrong, R. J. Mathar, Jul 14 2016]
G.f.: 1/(exp(x)-1). [Apparently not, R. J. Mathar, Jul 14 2016]
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[300], f[#] == 3 &] (* Amiram Eldar, Feb 15 2021 after Kevin Ryde at A161189 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
William J. Keith, Jul 17 2008, Jul 18 2008
STATUS
approved