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A051912 a(n) is the smallest integer such that the sum of any three ordered terms a(k), k <= n, is unique. 7
0, 1, 4, 13, 32, 71, 124, 218, 375, 572, 744, 1208, 1556, 2441, 3097, 4047, 5297, 6703, 7838, 10986, 12331, 15464, 19143, 24545, 28973, 34405, 37768, 45863, 50876, 61371, 68302, 77917, 88544, 101916, 122031, 131624, 148574, 171236, 197814 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Robert Israel, Table of n, a(n) for n = 0..100

EXAMPLE

Three terms chosen from {0,1,4} can be 0+0+0; 0+0+1; 0+1+1; 1+1+1; 0+0+4; 0+1+4; 1+1+4; 0+4+4; 1+4+4; 4+4+4 are all distinct (3*4*5/6 = 10 terms), so a(2) = 4 is the next integer of the sequence after 0 and 1.

MAPLE

A[0]:= 0: S:= {0}: S2:= {0}: S3:= {0}:

for i from 1 to 40 do

  for x from A[i-1] do

    if (map(t -> t+x, S2) intersect S3 = {}) and (map(t -> t+2*x, S) intersect S3 = {}) then

     A[i]:= x;

     S3:= S3 union map(t -> t+x, S2) union map(t -> t+2*x, S) union {3*x};

     S2:= S2 union map(t -> t+x, S) union {2*x};

     S:= S union {x};

     break

    fi

  od

od:

seq(A[i], i=0..40); # Robert Israel, Jul 01 2019

MATHEMATICA

a[0] = 0; a[1] = 1; a[n_] := a[n] = For[A0 = Array[a, n, 0]; an = a[n-1] + 1, True, an++, A1 = Append[A0, an]; A2 = Flatten[Table[A1[[{i, j, k}]], {i, 1, n+1}, {j, i, n+1}, {k, j, n+1}], 2]; A3 = Sort[Total /@ A2]; If[Length[A3] == Length[Union[A3]], Return[an]]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 0, 38}] (* Jean-Fran├žois Alcover, Nov 24 2016 *)

CROSSREFS

Cf. A025582, A036241, A062065.

Sequence in context: A212747 A011936 A037235 * A060099 A208638 A173277

Adjacent sequences:  A051909 A051910 A051911 * A051913 A051914 A051915

KEYWORD

nonn,nice

AUTHOR

Wouter Meeussen, Dec 17 1999

EXTENSIONS

More terms from Naohiro Nomoto, Jul 22 2001

STATUS

approved

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Last modified May 10 01:36 EDT 2021. Contains 343747 sequences. (Running on oeis4.)