cp's OEIS Frontend

A059868 There exist no palindromic pentagonal numbers of length a(n).

%I A059868 #28 Apr 15 2025 13:04:46
%S A059868 3,9,11,12,24,30,32,33
%N A059868 There exist no palindromic pentagonal numbers of length a(n).
%H A059868 Patrick De Geest, <a href="http://www.worldofnumbers.com/penta.htm">Palindromic pentagonals</a>
%t A059868 A002069 = {0, 1, 5, 22, 1001, 2882, 15251, 720027, 7081807, 7451547, 26811862, 54177145, 1050660501, 1085885801, 1528888251, 2911771192, 2376574756732, 5792526252975, 5875432345785, 10810300301801, 264571020175462, 5292834004382925, 10808388588380801, 15017579397571051, 76318361016381367, 150621384483126051, 735960334433069537, 1003806742476083001, 1087959810189597801, 2716280733370826172};
%t A059868 A059868[n_] := Length[Select[A002069, IntegerLength[#] == n  || (n == 1 && # == 0) &]];
%t A059868 Select[Range[18], A059868[#] == 0 &] (* _Robert Price_, Apr 26 2019 *)
%o A059868 (Python)
%o A059868 def ispal(n): s = str(n); return s == s[::-1]
%o A059868 def penpals(limit):
%o A059868   for k in range(limit+1):
%o A059868     if ispal(k*(3*k-1)//2): yield k*(3*k-1)//2
%o A059868 def aupto(limit):
%o A059868   lengths = set(range(1, limit+1))
%o A059868   for p in penpals(10**limit):
%o A059868     lp, minlen = len(str(p)), min(lengths)
%o A059868     for li in list(lengths):
%o A059868       if li < lp: print(li, "in A059868"); lengths.discard(li)
%o A059868     if lp in lengths: lengths.discard(lp); print("... discarding", lp)
%o A059868     if len(lengths) == 0: return
%o A059868 aupto(15) # _Michael S. Branicky_, Mar 09 2021
%Y A059868 Cf. A034822, A059869, A059870, A034307, A000326, A028386, A002069.
%K A059868 nonn,base,hard
%O A059868 1,1
%A A059868 _Patrick De Geest_, Feb 15 2000
%E A059868 Name clarified by _David A. Corneth_, Apr 26 2019
%E A059868 a(6)-a(8) from _Bert Dobbelaere_, Apr 15 2025