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 A208746 Size of largest subset of [1..n] containing no three terms in geometric progression. 7
 1, 2, 3, 3, 4, 5, 6, 7, 7, 8, 9, 10, 11, 12, 13, 13, 14, 14, 15, 15, 16, 17, 18, 19, 19, 20, 21, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 29, 30, 31, 32, 33, 34, 34, 35, 36, 37, 38, 38, 38, 39, 39, 40, 41, 42, 43, 44, 45, 46, 46, 47, 48, 49, 49, 50, 51, 52, 52, 53, 54, 55, 55, 56, 57, 57, 57, 58, 59, 60, 61, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 71, 72, 73, 74, 74, 75, 75, 75, 75 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS All three-term geometric progressions must be avoided, even those such as 4,6,9 whose ratio is not an integer. David Applegate's computation used a floating-point IP solver for the packing subproblems, so although it's almost certainly correct there is no proof. First he enumerated geometric progressions using for (i=1;i<=N;i++) {    for (j=2; j*j<=i; j++) {      if (i % (j*j) != 0) continue;      for (k=1; k x[t]+x[b]+x[b^2/t]<=2,           select(t -> (t=b^2/n),        numtheory:-divisors(b^2))), b=2..n-1)});      Optimization:-Maximize(add(x[i], i=1..n), cons, assume=binary)[1] end proc; CROSSREFS Cf. A003002. Sequence in context: A319413 A053207 A138467 * A230490 A247983 A127036 Adjacent sequences:  A208743 A208744 A208745 * A208747 A208748 A208749 KEYWORD nonn AUTHOR David Applegate and N. J. A. Sloane, Mar 01 2012 EXTENSIONS a(1)-a(82) confirmed by Robert Israel and extended to a(100), Mar 01 2012 STATUS approved

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Last modified January 18 01:36 EST 2019. Contains 319260 sequences. (Running on oeis4.)