A213918 a(n) = smallest possible element of a set of n positive integers s_1, s_2, ..., s_n such that for i != j, |s_i - s_j| = gcd(s_i, s_j), where |x| denotes absolute value.

1, 1, 2, 6, 36, 210, 14976, 552720, 309582000

Offset: 1

Author

Phil Scovis, Mar 04 2013

Keywords

• nonn
• more

Examples

			Examples of sets for the first few cases:
{1},
{1,2},
{2, 3, 4},
{6, 8, 9, 12},
{36, 40, 42, 45, 48},
{210, 216, 220, 224, 225, 240},
{14976, 14980, 14994, 15000, 15008, 15015, 15120},
{552720, 552825, 552960, 553000, 553014, 553140, 553280, 554400},
{309582000, 309583680, 309583800, 309583872, 309583890, 309584000, 309584025, 309584100, 309584160}.
		

Crossrefs

Cf. A061799, A214799.

Programs

Mathematica

ok[v_, n_] := v == Select[v, GCD[#, n] == Abs[n - #] &];
ric[p_, cc_, k_] :=
If[Length@p == k, sol = p; True,
  Block[{c = cc, x, r = False},
   While[c != {}, x = First@c; c = Rest@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@n] < k - 1 ||
!ric[{n}, n + d, k], n++]; n];
Do[Print[n, " ", a[n], " ", sol], {n, 7}]

Extensions

Corrected (with Mathematica program) by Giovanni Resta, Mar 05 2013. Entry revised by N. J. A. Sloane, Mar 05 2013

a(8) from Robert Gerbicz, Mar 05 2013

a(9) from Robert Gerbicz, Mar 06 2013