A082721 There exist no palindromic hexagonals of length n.

3, 8, 9, 12, 22, 24, 27, 30, 36, 38, 40

Offset

1,1

Links

Table of n, a(n) for n=1..11.

P. De Geest, Palindromic hexagonals

Mathematica

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};
A082721[n_] := Length[Select[A054969, IntegerLength[#] == n || (n == 1 && # == 0) &]];
Select[Range[19], A082721[#] == 0 &] (* Robert Price, Apr 27 2019 *)

Prog

(Python)
def ispal(n): s = str(n); return s == s[::-1]
def hexpals(limit):
  yield from (k*(2*k-1) for k in range(limit+1) if ispal(k*(2*k-1)))
def aupto(limit):
  lengths = set(range(1, limit+1))
  for h in hexpals(10**limit):
    if len(lengths) == 0: return
    lh, minlen = len(str(h)), min(lengths)
    if lh > minlen: print(minlen, "in A082721"); lengths.discard(minlen)
    if lh in lengths: lengths.discard(lh); print("... discarding", lh)
aupto(14) # Michael S. Branicky, Mar 08 2021

Crossrefs

Cf. A034822, A054969, A059868, A059869, A059870, A082722, A034307.

Sequence in context: A087286 A165289 A066494 * A239388 A259850 A071677

Adjacent sequences: A082718 A082719 A082720 * A082722 A082723 A082724

Keyword

nonn,base,hard,more

Author

Patrick De Geest, Apr 13 2003

Status

approved