This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A082721 #18 Aug 11 2024 14:41:34
%S A082721 3,8,9,12,22,24,27,30,36,38,40
%N A082721 There exist no palindromic hexagonals of length n.
%H A082721 P. De Geest, <a href="https://www.worldofnumbers.com/hexa.htm">Palindromic hexagonals</a>
%t A082721 A054969 = {0, 1, 6, 66, 3003, 5995, 15051, 66066, 617716, 828828, 1269621, 1680861, 5073705, 5676765, 1264114621, 5289009825, 6172882716, 13953435931, 1313207023131, 5250178710525, 6874200024786, 61728399382716, 602224464422206, 636188414881636, 1250444114440521, 16588189498188561, 58183932923938185, 66056806460865066, 67898244444289876, 514816979979618415, 3075488771778845703, 6364000440440004636, 15199896744769899151};
%t A082721 A082721[n_] := Length[Select[A054969, IntegerLength[#] == n || (n == 1 && # == 0) &]];
%t A082721 Select[Range[19], A082721[#] == 0 &] (* _Robert Price_, Apr 27 2019 *)
%o A082721 (Python)
%o A082721 def ispal(n): s = str(n); return s == s[::-1]
%o A082721 def hexpals(limit):
%o A082721 yield from (k*(2*k-1) for k in range(limit+1) if ispal(k*(2*k-1)))
%o A082721 def aupto(limit):
%o A082721 lengths = set(range(1, limit+1))
%o A082721 for h in hexpals(10**limit):
%o A082721 if len(lengths) == 0: return
%o A082721 lh, minlen = len(str(h)), min(lengths)
%o A082721 if lh > minlen: print(minlen, "in A082721"); lengths.discard(minlen)
%o A082721 if lh in lengths: lengths.discard(lh); print("... discarding", lh)
%o A082721 aupto(14) # _Michael S. Branicky_, Mar 08 2021
%Y A082721 Cf. A034822, A054969, A059868, A059869, A059870, A082722, A034307.
%K A082721 nonn,base,hard,more
%O A082721 1,1
%A A082721 _Patrick De Geest_, Apr 13 2003