

A307717


Number of palindromic squares, k^2, of length n such that k is also palindromic.


3



4, 0, 2, 0, 5, 0, 3, 0, 8, 0, 5, 0, 13, 0, 9, 0, 22, 0, 16, 0, 37, 0, 27, 0, 60, 0, 43, 0, 93, 0, 65, 0, 138, 0, 94, 0, 197, 0, 131, 0, 272, 0, 177, 0, 365, 0, 233, 0, 478, 0, 300, 0, 613, 0, 379, 0, 772, 0, 471, 0, 957, 0, 577, 0, 1170, 0, 698, 0, 1413, 0
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OFFSET

1,1


COMMENTS

Is a(2n) always zero?


LINKS

Table of n, a(n) for n=1..70.
P. De Geest, Palindromic Squares
Eric Weisstein's World of Mathematics, Palindromic Number


EXAMPLE

There are only two palindromic squares of length 3 whose root is also palindromic. 11^2=121 and 22^2=484. Thus, a(3)=2.


MATHEMATICA

Table[Length[Select[Range[If[n == 1, 0, Ceiling[Sqrt[10^(n  1)]]], Floor[Sqrt[10^n]]], # == IntegerReverse[#] && #^2 == IntegerReverse[#^2] &]], {n, 15}]


CROSSREFS

Cf. A002778, A002779, A034307, A034822.
Sequence in context: A319037 A067565 A243154 * A226782 A010635 A272198
Adjacent sequences: A307714 A307715 A307716 * A307718 A307719 A307720


KEYWORD

nonn,base,hard


AUTHOR

Robert Price, Apr 23 2019


EXTENSIONS

a(16)a(20) from Robert Price, Apr 25 2019
a(21)a(70) from Giovanni Resta, Apr 28 2019


STATUS

approved



