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A211316 Maximal size of sum-free set in additive group of integers mod n. 5
1, 1, 2, 2, 3, 2, 4, 3, 5, 4, 6, 4, 7, 6, 8, 6, 9, 6, 10, 7, 11, 8, 12, 10, 13, 9, 14, 10, 15, 10, 16, 12, 17, 14, 18, 12, 19, 13, 20, 14, 21, 14, 22, 18, 23, 16, 24, 16, 25, 18, 26, 18, 27, 22, 28, 19, 29, 20, 30, 20, 31, 21, 32, 26, 33, 22, 34, 24, 35, 24 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

REFERENCES

Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, Manuscript, May 2017. See Table in Section 1.6.1.

A. P. Street, Counting non-isomorphic sum-free sets, in Proc. First Australian Conf. Combinatorial Math., Univ. Newcastle, 1972, pp. 141-143.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 2..10000

Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, arXiv:1705.07444 [math.NT], May 2017. See Table in Section 1.6.1.

Ben Green and Imre Z. Ruzsa, Sum-free sets in abelian groups, arXiv:math/0307142 [math.CO], 2004.

FORMULA

If n is divisible by a prime == 2 mod 3 then a(n) = n(p+1)/(3p) where p is the smallest such prime divisor; otherwise if n is divisible by 3 then a(n) = n/3; otherwise all prime divisors of n are == 1 mod 3 and a(n) = (n-1)/3.

In particular, a(2n) = n (cf. A211317).

MATHEMATICA

a[n_] := Module[{f = FactorInteger[n][[All, 1]]}, For[i = 1, i <= Length[f], i++, If[Mod[f[[i]], 3]==2, Return[n*(f[[i]] + 1)/3/f[[i]]]]]; If[Mod[n, 3] == 1, n-1, n]/3]

Table[a[n], {n, 2, 100}] (* Jean-Fran├žois Alcover, Aug 02 2018, from PARI *)

PROG

(Haskell)

a211316 n | not $ null ps = n * (head ps + 1) `div` (3 * head ps)

          | m == 0        = n'

          | otherwise     = (n - 1) `div` 3

          where ps = [p | p <- a027748_row n, mod p 3 == 2]

                (n', m) = divMod n 3

-- Reinhard Zumkeller, Apr 25 2012

(PARI) a(n)=my(f=factor(n)[, 1]); for(i=1, #f, if(f[i]%3==2, return(n*(f[i]+1)/3/f[i]))); if(n%3, n-1, n)/3 \\ Charles R Greathouse IV, Sep 02 2015

CROSSREFS

Bisection: A211317. Cf. A007865, A027748, A003627.

Sequence in context: A178804 A322355 A242112 * A280226 A307995 A061889

Adjacent sequences:  A211313 A211314 A211315 * A211317 A211318 A211319

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 24 2012

STATUS

approved

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Last modified March 28 05:38 EDT 2020. Contains 333073 sequences. (Running on oeis4.)