A307752 Number of n-digit palindromic pentagonal numbers.

3, 1, 0, 2, 1, 1, 2, 2, 0, 4, 0, 0, 3, 1, 1, 1, 3, 2, 4, 1, 3, 1

Offset

1,1

Comments

Number of n-digit terms in A002069.

Links

Table of n, a(n) for n=1..22.

G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy] See page 95.

Example

There are only two 4-digit pentagonal number that are palindromic, 1001 and 2882. Thus, a(4)=2.

Mathematica

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};
Table[Length[Select[A002069, IntegerLength[#] == n  || (n == 1 && # == 0) &]], {n, 18}] (* Robert Price, Apr 26 2019 *)

Prog

(Python)
def afind(terms):
  m, n, c = 0, 1, 0
  while n <= terms:
    p = m*(3*m-1)//2
    s = str(p)
    if len(s) == n:
       if s == s[::-1]: c += 1
    else:
      print(c, end=", ")
      n, c = n+1, int(s == s[::-1])
    m += 1
afind(14) # Michael S. Branicky, Mar 01 2021

Crossrefs

Cf. A000326, A002069, A028386, A059868, A263618, A307717.

Sequence in context: A166408 A327077 A284826 * A101548 A117430 A354795

Adjacent sequences: A307749 A307750 A307751 * A307753 A307754 A307755

Keyword

nonn,base,more

Author

Robert Price, Apr 26 2019

Extensions

a(19)-a(22) from Michael S. Branicky, Mar 01 2021

Status

approved