Your starting example is presumably a Borgnine.
M

On 10/04/2021 23:03, 'Nollaig MacKenzie' via Chat wrote:
Generalizing recklessly from the single example, 7 of 9,
I conjectured that

      borgnum n

would be the greatest prime less than n^2

Looking for a J expression took me to:

      borgnum=:p:@(<:@(p:^:_1))@*:

whence the 1st 10 borg numbers are

3 7 13 23 31 47 61 79 97 113

What was pleasing, of course, was the way p:^:_1 gave just what I wanted.

I checked OEIS.org, and, indeed, the sequence is there, A053001, not, alas,
identified as the borg numbers.

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