1,2

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 (jvospost3(AT)gmail.com) 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 (jhbubby(AT)mindspring.com), Oct 02 2006 remarks that n = 1, 2, 4, 5 and 10 have this property and conjectures that there are no other values.

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

# a[n] = n-th term of sequence, m[n] = a[n]/n = A122543(n) (Maple program from njas)

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)];

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] (*Chandler*)

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

Sequence in context: A025618 A133572 A121852 this_sequence A059736 A102731 A007179

Adjacent sequences: A122534 A122535 A122536 this_sequence A122538 A122539 A122540

nonn

J. Lowell (jhbubby(AT)mindspring.com), Sep 18 2006

More terms from njas and Chai Tian (Chao.Tian(AT)epfl.ch), Sep 19 2006