Had pure fun writing this :)

First I calculated hex(11) in my head, took about half an hour.

Then I tried to make sense of the sequence the best I could before
looking up the closed form.

bin/hex.py

@@ -0,0 +1,71 @@
+#!/usr/bin/env python3
+# https://click.palletsprojects.com/en/8.1.x/arguments/
+# https://click.palletsprojects.com/en/8.1.x/options/
+
+import click
+import math
+import sys
+
+# I'm not proud (I am a little bit?).
+PROOF = [] # :)
+
+class AgoraCmd(click.Command):
+    def format_help(self, ctx, formatter):
+        click.echo("""Usage:
+        - Visit anagora.org/primes to execute this file in the Agora of Flancia.
+        - Visit e.g. anagora.org/primes/17 to test if 17 is prime.
+        - In general visit anagora.org/foo, anagora.org/foo/bar to execute e.g. <bin/foo.py bar> from your garden.
+        """)
+
+    def __call__(self, *args, **kwargs):
+        try:
+            return super(AgoraCmd, self).__call__(
+                *args, standalone_mode=False, **kwargs)
+        except click.MissingParameter as exc:
+            exc.ctx = None
+            exc.show(file=sys.stdout)
+            click.echo()
+            try:
+                super(AgoraCmd, self).__call__(['--help'])
+            except SystemExit:
+                sys.exit(exc.exit_code)
+
+@click.command(cls=AgoraCmd)
+@click.argument('n', type=click.INT)
+def hexnum(n, centered=True):
+    """Calculates the first n hex numbers: buggy for now, it both under- and over-prints :)."""
+
+    # Going through this from first principles (from memory/deducing this) for fun :) 
+
+    # Why does the first list comprehension I wrote knowing it was wrong not work? 
+    # Is it because of its complexity? Note I don't know the 'closed form' for hex numbers yet but I think it exists.
+    # To calculate them, I only know you need to add 6 more than after the previous number. 
+    # But that can't be (trivially) expressed in a list comprehension.
+    # 
+    # hexnums = [int(centered) + 6*n for n in range(0,n)]
+    # click.echo(f"These are not all hex numbers, but some are: {list(enumerate(hexnums))}")
+
+    # If we could skip one, then two, then three from the list above, 
+    # we could exclude all non-hex-numbers.
+    # is there something in itertools that can do this for us?
+    # I don't think so. Maybe dropwhile with the right lambda?
+
+    # ...anyway, going at it old school.
+    # acc = int(centered)
+    # for row in range(0, n+1):
+    #     acc += 6 * row
+    #     click.echo(f"hex({row}) is {acc}.")
+
+    # ...and then https://oeis.org/A003215 to the rescue :)
+    # [[crystal ball sequence for hexagonal lattice]]: why does this work?
+    # -> https://en.wikipedia.org/wiki/Centered_hexagonal_number
+    # It is a cubic polynomial and Wikipedia shows how to convince yourself that it works. 
+    # Beautiful :)
+    hexnums = [3*n*(n+1)+1 for n in range(0,n+1)]
+
+    for nth, hexnum in enumerate(hexnums):
+        click.echo(f"hex({nth}) is {hexnum}.")
+
+
+if __name__ == '__main__':
+    hexnum()