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 A034463 Maximal number of residue classes mod n such that no subset adds to 0. 0
 0, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 9, 10, 10, 10, 10, 10, 10, 10, 10, 11, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS From Jon E. Schoenfield, Jun 13 2010: (Start) Given a value of n, one way to obtain a set of residue classes having no zero subset sum is simply to select the first k positive integers, where k is the largest integer such that sum(1..k)0, this yields a set of k residue classes where k=round(sqrt(2n))-1, which serves as a first lower bound for a(n). For n>5, another simple method is to select the residue classes 1, n-2, and 3..k, where k is the largest integer such that sum(1..k)-2=7, a(75)>=12, a(375)>=27, a(525)>=32, a(1125)>=47, a(1375)>=52, etc. For each of the first 87 terms in the sequence, an exhaustive search determined that a(n) either equals the first lower bound (round(sqrt(2n))-1) or exceeds it by only 1, and that at least one of the four methods above yields a maximal solution. The sequence is not nondecreasing; a(n)= 6 (in fact a(20)=6). For n=30, {1,2,3,4,5,6,7} shows that a(30)>=7 (in fact a(30)=7). PROG (PARI) a(n)=my(v=vector(n, i, i), t, w, r); for(i=1, 2^(n-1)-1, if(hammingweight(i)<=r, next); t=vecextract(v, i); w=vector(n); w[1]=1; for(j=1, #t, w+=concat(w[t[j]+1..n], w[1..t[j]]); if(w[1]>1, next(2))); r=hammingweight(i)); r \\ Charles R Greathouse IV, Oct 16 2013 CROSSREFS Sequence in context: A162988 A143824 A182009 * A259899 A071996 A072747 Adjacent sequences:  A034460 A034461 A034462 * A034464 A034465 A034466 KEYWORD nonn,nice AUTHOR EXTENSIONS The reference gives a(5)=3, but this is incorrect, a(5)=2. More terms from John W. Layman, Oct 02 2002 Terms a(36)-a(87) from Jon E. Schoenfield, Jun 13 2010 STATUS approved

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Last modified May 22 21:02 EDT 2019. Contains 323499 sequences. (Running on oeis4.)