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

1,2

Comments

The definition: "a(1) = 1; for n>1, a(n) is smallest number greater than a(n-1) and not equal to any a(i)+a(j) with i and j <= n-1" produces the odd numbers 1, 3, 5, ...

Jonathan Vos Post asks if 1, 2, 4 and 5 are the only values of n for which n^2 divides a(n), Sep 19 2006. J. Lowell, Oct 02 2006 remarks that n = 1, 2, 4, 5 and 10 have this property and conjectures that there are no other values.

Links

Table of n, a(n) for n=1..51.

Example

The 5th term cannot be 20 because 20 = 16+4 and 16 and 4 are both in the sequence.

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)];

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 *)

Crossrefs

Cf. A122543 (a(n)/n), A002858, A122544, A122545, A122804.

Sequence in context: A121852 A321411 A242251 * A059736 A261682 A102731

Adjacent sequences: A122534 A122535 A122536 * A122538 A122539 A122540

Keyword

nonn

Author

J. Lowell, Sep 18 2006

Extensions

More terms from N. J. A. Sloane and Chai Tian (Chao.Tian(AT)epfl.ch), Sep 19 2006

Status

approved