[seqfan] Re: Phil Scovis's problem

[T. D. Noe]

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
>
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>
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Tony Noe                  | voice:     503-690-2099
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