A307752 - OEIS

%I #18 Mar 02 2021 02:04:10

%S 3,1,0,2,1,1,2,2,0,4,0,0,3,1,1,1,3,2,4,1,3,1

%N Number of n-digit palindromic pentagonal numbers.

%C Number of n-digit terms in A002069.

%H G. J. Simmons, <a href="/A002778/a002778_2.pdf">Palindromic powers</a>, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy] See page 95.

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

%t 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 Table[Length[Select[A002069, IntegerLength[#] == n  || (n == 1 && # == 0) &]], {n, 18}] (* _Robert Price_, Apr 26 2019 *)

%o (Python)

%o def afind(terms):

%o   m, n, c = 0, 1, 0

%o   while n <= terms:

%o     p = m*(3*m-1)//2

%o     s = str(p)

%o     if len(s) == n:

%o        if s == s[::-1]: c += 1

%o     else:

%o       print(c, end=", ")

%o       n, c = n+1, int(s == s[::-1])

%o     m += 1

%o afind(14) # _Michael S. Branicky_, Mar 01 2021

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

%K nonn,base,more

%O 1,1

%A _Robert Price_, Apr 26 2019

%E a(19)-a(22) from _Michael S. Branicky_, Mar 01 2021