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

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Ali Sada

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Jun 14, 2026, 12:59:59 AM (10 days ago) Jun 14
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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 , the interval is . The representable values are

For , the interval is . The representable values are


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


Best,

Ali 

Stefano Spezia

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Jun 14, 2026, 2:54:14 AM (10 days ago) Jun 14
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In my opinion, the sequence is enough interesting to be included. The next two terms are 3579, 6397.

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


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Robert Israel

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Jun 14, 2026, 9:15:00 AM (10 days ago) Jun 14
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In my opinion, alternative #2 is better.  Let's not "consider" things that violate standard mathematical terminology.

Ali Sada

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Jun 14, 2026, 10:42:46 AM (10 days ago) Jun 14
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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 

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