This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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: A066508 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.