This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a = {0, 1, 1}; Do[AppendTo[a, If[MemberQ[a, c = Quotient[a[[-1]], 3]], a[[-1]] + a[[-2]], c]], {n, 3, 59}]; Delete[a, 1] (* Ivan Neretin, Sep 04 2015 *)
R:= 2: S:= {2}: a:= 2:
for n from 2 to 100 do
t:= floor(a/2);
if t <> 0 and not member(t,S) then a:= t else a:= 2*n fi;
R:= R,a; S:= S union {a};
od:
R; # Robert Israel, Aug 03 2025
a(6) = 4, and all divisors of 4 are already used, hence a(7) = a(6) + a(5) = 8 + 4 = 12. Now the smallest unused divisor of 12 is 6, hence a(8) = 6.
Nest[Append[#, If[(d = Complement[Divisors@#[[-1]], #]) == {}, #[[-1]] + #[[-2]], Min[d]]] &, {1, 2}, 63]
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