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 A341584 Size of the largest subset of the numbers [1..n] which does not contain a 3-term arithmetic progression modulo n. 0
 0, 1, 2, 2, 2, 2, 4, 3, 4, 4, 4, 4, 4, 4, 6, 4, 6, 5, 8, 6, 8, 6, 8, 6, 8, 7, 8, 8, 8, 8, 8, 8, 9, 8, 10, 9, 10, 10, 12, 10, 11, 9, 12, 9, 12, 10, 12, 10, 13, 10, 14, 11, 14, 11, 16, 11, 16, 12, 16, 12, 16, 13, 16, 13, 16, 14, 16, 13, 16, 14, 18, 14, 16, 14, 20, 14, 16, 14, 20, 15, 18 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This is similar to A003002, but the arithmetic progression is modulo n here. For n >= 3, a(n) can be viewed as the maximum number of vertices that can be chosen from a regular polygon with n sides so that no three of them form an isosceles or equilateral triangle. LINKS Math StackExchange, A question about this sequence. EXAMPLE n, a(n), example of an optimal subset: 0, 0, {} 1, 1, {1} 2, 2, {1,2} 3, 2, {1,2} 4, 2, {1,2} 5, 2, {1,2} 6, 4, {1,2,4,5} 7, 3, {1,2,4} 8, 4, {1,2,4,5} 9, 4, {1,2,4,5} 10, 4, {1,2,4,5} 11, 4, {1,2,4,5} 12, 4, {1,2,4,5} 13, 4, {1,2,4,5} 14, 6, {1,2,4,8,9,11} 15, 4, {1,2,4,5} 16, 6, {1,3,4,8,9,11} 17, 5, {1,2,6,7,9} 18, 8, {1,2,4,5,10,11,13,14} 19, 6, {1,3,4,8,9,11} 20, 8, {1,2,4,5,11,12,14,15} PROG (C) /* For n >= 3: */ int a(int n) { int upp, maxb, s, i, l, h, maxs; uint64_t b, bs, m, mv[31], mn; for (l = 1; l <= 31; l++) { mv[l - 1] = 1 << 2*l; mv[l - 1] |= (1 << l); mv[l - 1] |= 1; } maxb = 1 << n; mn = maxb - 1; h = (n - 1) / 2; maxs = 2*n/3; upp = 0; for (b = 0; b < maxb; b++) {   for (i = 0, s = 0, m = 1; i < n; i++, m <<= 1) { if (b & m) s++; }   if (s <= maxs) {    for (l = 1; l <= h; l++) {     m = mv[l - 1];     for (i = 0; i < n; i++) { if ((b & m) == m) { l = 1000; break; } m = ((m << 1) & mn) | (m >> (n - 1)); }    }    if (l < 1000 && s > upp) upp = s;   } } return upp; } CROSSREFS Cf. A003002. Sequence in context: A098983 A097576 A029250 * A110884 A303637 A155904 Adjacent sequences:  A341581 A341582 A341583 * A341585 A341586 A341587 KEYWORD nonn,more AUTHOR Fabio VisonĂ , Feb 15 2021 EXTENSIONS a(31)-a(80) from Bert Dobbelaere, Feb 20 2021 STATUS approved

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Last modified May 5 23:41 EDT 2021. Contains 343579 sequences. (Running on oeis4.)