A263617 Number of numbers with at most n digits whose square is a palindrome.

4, 7, 15, 20, 31, 37, 56, 70, 95, 113, 162, 193, 264, 310, 415, 486, 640, 741, 950, 1082, 1374, 1556, 1940, 2176, 2673, 2975, 3611, 3994, 4793, 5268, 6249, 6827, 8028, 8729

Offset: 1

Author

N. J. A. Sloane, Oct 23 2015

Keywords

• nonn
• base
• more

Links

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

Crossrefs

Partial sums of A263616.

Cf. A002778, A002779, A263618, A263619.

Programs

Mathematica

Table[Length[Select[Range[ 0, 10^n - 1], PalindromeQ[#^2] &]], {n, 6}] (* Robert Price, Apr 26 2019 *)

Extensions

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

a(11)-a(12) from Michael S. Branicky, May 23 2021

a(13)-a(22) (using A002778) from Chai Wah Wu, Sep 16 2021

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