[seqfan] Re: Phil Scovis's problem

[Neil Sloane]

The "triangle" of solutions (to any of the three problems) is probably not
well-defined, because there may be more than one solution. However, the
triangles giving the lexicographically earliest solutions would be OK to
submit.

On Tue, Mar 5, 2013 at 2:32 PM, T. D. Noe <noe at sspectra.com> wrote:

> The author asked that it be removed.  Please submit the triangle.
>
> Tony
>
>
> At 8:28 PM +0100 3/5/13, Giovanni Resta wrote:
> >On 03/05/2013 07:14 PM, Neil Sloane wrote:
> >
> >> Definition. Let S be a set of n positive numbers such that
> >> all n choose 2 pairwise GCD's are distinct.
> >
> >That was my first interpretation of the sequence's name.
> >
> >However, after looking at the data (which was wrong but not so wrong),
> >I guessed the intended meaning:
> >
> >Scovis: "Minimum element in a set of positive integers of size n where
> >every pair of elements differs by their GCF".
> >
> >Meaning:
> >Minimum possible element of a set of n positive integers a_1,a_2,...,a_n
> >such that for i != j,  |a_i - a_j| = GCD(a_i, a_j), where |x| denote
> >the absolute value of x.
> >
> >I have computed the first sets, which give the sequence 1, 1, 2, 6, 36,
> >210, 14976, ... where the sets are:
> >{1}, {1,2}, {2, 3, 4}, {6, 8, 9, 12}, {36, 40, 42, 45, 48}, {210, 216,
> >220, 224, 225, 240}, and {14976, 14980, 14994, 15000, 15008, 15015,
> 15120}.
> >
> >But in the meantime the sequence disappeared....
> >
> >The Mma program I used is the following:
> >
> >ok[v_, n_] := v == Select[v, GCD[#, n] == Abs[n - #] &];
> >
> >ric[p_, cc_, k_] :=
> >  If[Length at p == k, sol = p; True,
> >   Block[{c = cc, x, r = False},
> >    While[c != {}, x = First at c; c = Rest at c;
> >     If[p == Select[p, GCD[#, x] == Abs[x - #] &] &&
> >      ric[Append[p, x], c, k], r = True; Break[]]]; r]];
> >
> >a[k_] := Block[{n = 1, d}, While[Length[d = Divisors at n] < k - 1 ||
> >  !ric[{n}, n + d, k], n++]; n];
> >
> >Do[Print[n, " ", a[n], " ", sol], {n, 7}]
> >
> >Giovanni Resta
> >
> >_______________________________________________
> >
> >Seqfan Mailing list - http://list.seqfan.eu/
>
> --
>
> Tony Noe                  | voice:     503-690-2099
> Software Spectra, Inc.    | fax:       503-690-8159
> 14025 N.W. Harvest Lane   | e-mail:    noe at sspectra.com
> Portland, OR  97229, USA  | Web site:  http://www.sspectra.com
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com