A263618 - OEIS

%I #26 Jun 15 2024 13:08:06

%S 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,

%T 0,70,1,153,1,98,3,209,0,132,0,291,1,181,1

%N Number of palindromic squares with exactly n digits.

%C Number of terms in A002779 with exactly n digits.

%C a(24) = a(30) = a(38) = a(40) = 0. - _Robert Price_, Apr 26 2019

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

%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.

%t 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 *)

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

%Y Cf. A034822 (positions of zeros).

%K nonn,base,more

%O 1,1

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

%E a(13)-a(19) from _Chai Wah Wu_, Oct 24 2015

%E a(20) from _Robert Price_, Apr 26 2019

%E a(21)-a(44) (using A002778) from _Chai Wah Wu_, Sep 16 2021