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Number of n-digit numbers whose square is a palindrome.
1

%I #21 Sep 16 2021 12:20:43

%S 4,3,8,5,11,6,19,14,25,18,49,31,71,46,105,71,154,101,209,132,292,182

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

%C Number of terms in A002778 with exactly n digits.

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

%t 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 *)

%o (Python)

%o from itertools import product

%o def pal(n): s = str(n); return s == s[::-1]

%o def a(n): return int(n==1) + sum(pal(i**2) for i in range(10**(n-1), 10**n))

%o print([a(n) for n in range(1, 8)]) # _Michael S. Branicky_, Apr 03 2021

%Y Cf. A002778, A002779, A263617, A263618.

%K nonn,base,more

%O 1,1

%A _N. J. A. Sloane_, Oct 23 2015

%E a(9)-a(10) from _Chai Wah Wu_, Oct 25 2015

%E a(11) from _Michael S. Branicky_, Apr 03 2021

%E a(12)-a(22) (using A002778) from _Chai Wah Wu_, Sep 16 2021