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A211316
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Maximal size of sum-free set in additive group of integers mod n.
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3
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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
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OFFSET
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2,3
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REFERENCES
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Ben Green and Imre Z. Ruzsa, Sum-free sets in abelian groups, arXiv:math/0307142, 2004.
A. P. Street, Counting non-isomorphic sum-free sets, in Proc. First Australian Conf. Combinatorial Math., Univ. Newcastle, 1972, pp. 141-143.
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 2..10000
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FORMULA
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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).
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PROG
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(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
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CROSSREFS
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Bisection: A211317. Cf. A007865.
Cf. A027748, A003627.
Sequence in context: A205378 A103391 A178804 * A061889 A218700 A175012
Adjacent sequences: A211313 A211314 A211315 * A211317 A211318 A211319
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Apr 24 2012
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STATUS
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approved
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