What if all square roots of integers were "integers"?

[Ali Sada]

Hi everyone,

Hope all is well. Is this an acceptable OEIS sequence? 

"Number of "integers" in [n,n+1) if every square root of a positive integer is also considered an integer."

Or 

"Number of distinct values in the interval [n,n+1) that can be represented as a finite sum of square roots of positive integers."

For n=1, the interval is [1,2). The representable values are

1, sqrt(2), and sqrt(3). So a(1) = 3.

For n=2, the interval is [2,3). The representable values are

2,1+sqrt(2), 1+sqrt(3), sqrt(5), sqrt(6), sqrt(7), and sqrt(8). So, a(2) = 7.

3,7,17,35,76,148,295,564,1068,1965

Best,

Ali 

[Stefano Spezia]

In my opinion, the sequence is enough interesting to be included. The next two terms are 3579, 6397.

Inviato da iPad

Il giorno 14 giu 2026, alle ore 07:00, Ali Sada <ali....@gmail.com> ha scritto:



--
You received this message because you are subscribed to the Google Groups "SeqFan" group.
To unsubscribe from this group and stop receiving emails from it, send an email to seqfan+un...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/seqfan/CACOfRNqvQFpuyiqhPFMkV2iJr%2BOFdBL6%3DSMA7gwSxxqTGemzqg%40mail.gmail.com.

[Robert Israel]

In my opinion, alternative #2 is better.  Let's not "consider" things that violate standard mathematical terminology.

To view this discussion visit https://groups.google.com/d/msgid/seqfan/5D15B0AA-EAF7-4550-9C78-5AD6AB33AAF8%40gmail.com.

[Ali Sada]

Thank you very much Stefano and Robert for your responses. I really appreciate them. The proposed sequence is https://oeis.org/draft/A397045.

Best,

Ali 

To view this discussion visit https://groups.google.com/d/msgid/seqfan/CAJ3jLkw%2ByXwv%3DC10ODNuABfOGpbkBxLu9OxgjYP1H59gFdkL%3DQ%40mail.gmail.com.