A122537 a(1) = 1; for n>1, a(n) is smallest number greater than a(n-1), divisible by n and not equal to any a(i)+a(j) with i and j <= n-1.
1, 4, 6, 16, 25, 30, 35, 40, 45, 100, 110, 120, 143, 154, 180, 192, 204, 216, 228, 260, 294, 330, 345, 480, 500, 572, 594, 616, 638, 720, 744, 768, 858, 884, 945, 1008, 1036, 1102, 1131, 1160, 1189, 1218, 1247, 1320, 1395, 1426, 1457, 1584, 1617, 1700, 1734
Offset: 1
Keywords
Examples
The 5th term cannot be 20 because 20 = 16+4 and 16 and 4 are both in the sequence.
Programs
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Maple
# a[n] = n-th term of sequence, m[n] = a[n]/n = A122543(n) (Maple program from N. J. A. Sloane) a:=array(0..100000); m:=array(0..100000); hit:=array(0..100000); B:=100000; M:=100; for n from 1 to B do hit[n]:=0; od: a[1]:=1; m[1]:=1; a[2]:=4; m[2]:=2; hit[2]:=1; hit[5]:=1; hit[8]:=1; for n from 3 to M do i:=n*(floor(a[n-1]/n))+n; while hit[i] = 1 do i:=i+n; od; a[n]:= i; m[n]:= i/n; for j from 1 to n do hit[a[j]+i]:=1; od: od: [seq(a[n],n=1..M)]; [seq(m[n],n=1..M)];
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Mathematica
f[s_] := Block[{n, k},n = Length[s] + 1;k = Last[s] + n - Mod[Last[s], n];While[MemberQ[Union[Plus @@@ Tuples[s, 2]], k], k += n];Append[s, k]];Nest[f, {1}, 51] (* Ray Chandler, Sep 29 2006 *)
Extensions
More terms from N. J. A. Sloane and Chai Tian (Chao.Tian(AT)epfl.ch), Sep 19 2006
Comments