A307753 Number of palindromic pentagonal numbers of length n whose index is also palindromic.

3, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,1

Comments

Is there a nonzero term beyond a(5)?

Links

Table of n, a(n) for n=1..35.

P. De Geest, Palindromic Squares

Eric Weisstein's World of Mathematics, Palindromic Number

Example

There is only one palindromic pentagonal number of length 4 whose index is also palindromic, 44->2882. Thus, a(4)=1.

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};
A028386 = {0, 1, 2, 4, 26, 44, 101, 693, 2173, 2229, 4228, 6010, 26466, 26906, 31926, 44059, 1258723, 1965117, 1979130, 2684561, 13280839, 59401650, 84885761, 100058581, 225563533, 316882086, 700457153, 818049201, 851649306, 1345679688};
Table[Length[Select[A028386[[Table[Select[Range[18], IntegerLength[A002069[[#]]] == n  || (n == 1 && A002069[[#]] == 0) &], {n, 18}][[n]]]], PalindromeQ[#] &]], {n, 18}]

Crossrefs

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

Sequence in context: A366725 A122960 A242887 * A181116 A051834 A121383

Adjacent sequences: A307750 A307751 A307752 * A307754 A307755 A307756

Keyword

nonn,base,hard,more

Author

Robert Price, Apr 26 2019

Extensions

a(19)-a(35) from Chai Wah Wu, Sep 07 2019

Status

approved