A263616 Number of n-digit numbers whose square is a palindrome.

4, 3, 8, 5, 11, 6, 19, 14, 25, 18, 49, 31, 71, 46, 105, 71, 154, 101, 209, 132, 292, 182, 384, 236, 497, 302, 636, 383, 799, 475, 981, 578, 1201, 701

Offset: 1

Author

N. J. A. Sloane, Oct 23 2015

Keywords

• nonn
• base
• more

Comments

Number of terms in A002778 with exactly n digits.

Examples

			a(2) = 3 because there are three 2-digit numbers with palindromic squares: 11^2 = 121, 22^2 = 484, 26^2 = 676.
		

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, A263618, A263619.

Programs

Mathematica

Join[{4},Table[Total[Table[If[PalindromeQ[n^2],1,0],{n,10^x,10^(x+1)-1}]],{x,9}]] (* Harvey P. Dale, Apr 09 2019 *)

Python

from itertools import product
def pal(n): s = str(n); return s == s[::-1]
def a(n): return int(n==1) + sum(pal(i**2) for i in range(10**(n-1), 10**n))
print([a(n) for n in range(1, 8)]) # Michael S. Branicky, Apr 03 2021

Extensions

a(9)-a(10) from Chai Wah Wu, Oct 25 2015

a(11) from Michael S. Branicky, Apr 03 2021

a(12)-a(22) (using A002778) from Chai Wah Wu, Sep 16 2021

a(23)-a(34) from A002778 added by Max Alekseyev, Apr 08 2025