A358370 a(n) is the size of the largest 3-independent set in the cyclic group Zn.

0, 0, 0, 1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 3, 5, 3, 5, 4, 6, 5, 6, 4, 7, 5, 7, 5, 8, 6, 8, 7, 9, 6, 9, 6, 10, 7, 10, 7, 11, 9, 11, 8, 12, 8, 12, 9, 13, 9, 13, 11, 14, 9, 14, 10, 15, 10, 15, 10, 16, 13, 16, 11, 17, 12, 17, 12, 18, 12, 18, 15, 19, 14

Offset

1,8

Links

Table of n, a(n) for n=1..77.

Béla Bajnok, Additive Combinatorics in Groups and Geometric Combinatorics on Spheres, arXiv:2211.01890 [math.NT], 2022. See p. 4.

Béla Bajnok and Imre Ruzsa, The independence number of a subset of an abelian group. Integers, 3 (2003), Paper A2. See p. 5.

Formula

a(n) = floor(n/4) if n is even, a(n) = (1 + 1/p)*n/6 if n is odd with smallest prime divisor p congruent 5 mod 6, and a(n) = floor(n/6) otherwise.

Mathematica

b[n_]:=Min[Intersection[Divisors[n], Select[Prime[Range[PrimePi[n]]], Mod[#, 6]==5 &]]]; a[n_]:=If[EvenQ[n], Floor[n/4], If[IntegerQ[b[n]], (1+1/b[n])n/6, Floor[n/6]]]; Array[a, 80]

Crossrefs

Cf. A002265, A007528, A027750, A152467.

Sequence in context: A029363 A304708 A367758 * A319688 A033922 A008624

Adjacent sequences: A358367 A358368 A358369 * A358371 A358372 A358373

Keyword

nonn,easy

Author

Stefano Spezia, Nov 12 2022

Status

approved