A conjecture?/formula? in A003602 and A001511

[Sela Fried]

On the same day -  Nov 21 2015 - L. Edson Jeffery wrote

A003602(n) = A181988(n)/A001511(n)

A001511(n) = A181988(n)/A003602(n)

once as a formula and once as a conjecture, in the respective sequences. Both statements are equal and true. The proof is trivial. What should be done with this?

[Antti Karttunen]

Well, just remove that "Conjecture: " from the beginning in A001511, like I had done in A181988.

On the defense of Edson I have to say that the original definition of A181988 was more obscure, so it was probably not so clear then.

 

Best regards,

Antti

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[Sela Fried]

I'll do that. Of course, I meant no disrespect and actually I think that "trivial" wasn't actually adequate here. 

‫בתאריך יום ב׳, 1 בדצמ׳ 2025 ב-11:32 מאת ‪Antti Karttunen‬‏ <‪antti.k...@gmail.com‬‏>:‬

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[M F Hasler]

On Mon, Dec 1, 2025 at 5:37 AM Sela Fried <frie...@gmail.com> wrote:

I'll do that. Of course, I meant no disrespect and actually I think that "trivial" wasn't actually adequate here. 

Well, in A181988 we have:

FORMULA
a((2*n-1)*2^p) = n*(p+1), p >= 0.  (without date => since the entry was created)

a(n) = A001511(n)*A003602(n). - L. Edson Jeffery, Nov 21 2015. [Follows directly from above formula. - Antti Karttunen, Jan 19 2016]

I think Antti's comment is true ("p" in the first FORMULA is exactly the definition of A001511,

and A003602 has definition and 1st FORMULA:  a(n) = (A000265(n) + 1)/2)

to the point that it (the comment) isn't really necessary, IMO.

And I don't think how the two other formulas (a=b*c  =>  b=a/c  and  c=a/b) 

would not be trivial at this point (i.e., right when A181988 with the initial FORMULA was created).

- Maximilian

‫בתאריך יום ב׳, 1 בדצמ׳ 2025 ב-11:32 מאת ‪Antti Karttunen‬‏ <‪antti.k...@gmail.com‬‏>

On Mon, Dec 1, 2025 at 11:15 AM Sela Fried <frie...@gmail.com> wrote:

On the same day -  Nov 21 2015 - L. Edson Jeffery wrote
A003602(n) = A181988(n)/A001511(n)

A001511(n) = A181988(n)/A003602(n)

Well, just remove that "Conjecture: " from the beginning in A001511, like I had done in A181988.