A263618 Number of palindromic squares with exactly n digits.

4, 0, 3, 0, 7, 1, 5, 0, 11, 0, 5, 1, 19, 0, 13, 1, 25, 0, 18, 0, 48, 1, 31, 0, 70, 1, 44, 2, 105, 0, 70, 1, 153, 1, 98, 3, 209, 0, 132, 0, 291, 1, 181, 1, 384, 0, 234, 2, 496, 1, 301, 1, 636, 0, 383, 0, 798, 1, 474, 1, 981, 0, 578, 0, 1199, 2, 701

Offset: 1

Author

N. J. A. Sloane, Oct 23 2015

Keywords

• nonn
• base
• more

Comments

Number of terms in A002779 with exactly n digits.

a(24) = a(30) = a(38) = a(40) = 0. - Robert Price, Apr 26 2019

a(2*k+1) > 0 since (10^k+1)^2 is a palindrome of 2*k+1 digits. - Chai Wah Wu, Jun 14 2024

Links

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

Crossrefs

Cf. A002778, A002779, A263617, A263617, A263619, A263620.

Cf. A034822 (positions of zeros).

Programs

Mathematica

Table[Length[Select[Range[If[n == 1, 0, Ceiling[Sqrt[10^(n - 1)]]],Floor[Sqrt[10^n]]], #^2 == IntegerReverse[#^2] &]], {n, 15}] (* Robert Price, Apr 26 2019 *)

Extensions

a(13)-a(19) from Chai Wah Wu, Oct 24 2015

a(20) from Robert Price, Apr 26 2019

a(21)-a(44) (using A002778) from Chai Wah Wu, Sep 16 2021

a(45)-a(67) from A002778 added by Max Alekseyev, Apr 08 2025