Should A016789 and A033627 be cross-referenced?

[Ali Sada]

Hi everyone, 

 

Hope all is well. A033627 is “0-additive sequence: not the sum of any previous pair,”  while A016789 (with a(0) = 1) could be “a(0) = 1, a(1) = 2; for n ≥ 2 a(n) not the sum of any not-necessarily-distinct previous pair.”

 

Best,

 

Ali

[M F Hasler]

On Tue, Jun 2, 2026 at 9:18 PM Ali Sada <ali....@gmail.com> wrote:

Hope all is well. A033627 is “0-additive sequence: not the sum of any previous pair,”  while A016789 (with a(0) = 1) could be “a(0) = 1, a(1) = 2; for n ≥ 2 a(n) not the sum of any not-necessarily-distinct previous pair.”

I agree: they should xref each other. I proposed an edit in that sense (with formula & xref).

You should do the same in the future, when you spot an obvious equality/relation between 2 sequences, which is not yet mentioned.

(Such a simple contribution should usually be immediately approved by the editors so it shouldn't take up one of your editing slots for long, if that is a concern.)

I'm somewhat sceptical about the second proposal since the sequence has not a(0)=1 but a(0)=2.

(So, do you mean all terms should be shifted? OK, I think you can propose a comment saying that

"If a 1 is prefixed to the terms, then all terms are always the smallest positive integer not equal to a previous term or sum of two [not necessarily distinct] previous terms."

(And if I'm not wrong one can omit "a previous term" if we prefix both, 0 and 1.

Actually, it seems quite obvious (trivial?) that 0 & 1 yield 2 as next term, and then since a(n)+{0, 1, 2} (and smaller) are forbidden, a(n)+3 is always the next term.)

- Maximilian