A213918 - OEIS

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

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

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}.

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}]

CROSSREFS

Cf. A061799, A214799.

Sequence in context: A101609 A281024 A152668 * A239889 A086325 A343581

Adjacent sequences: A213915 A213916 A213917 * A213919 A213920 A213921

KEYWORD

nonn,more

AUTHOR

Phil Scovis, Mar 04 2013

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

STATUS

approved