A263619 Number of palindromic squares with at most n digits.

4, 4, 7, 7, 14, 15, 20, 20, 31, 31, 36, 37, 56, 56, 69, 70, 95, 95, 113, 113, 161, 162, 193, 193, 263, 264, 308, 310, 415, 415, 485, 486, 639, 640, 738, 741, 950, 950, 1082, 1082, 1373, 1374, 1555, 1556, 1940, 1940, 2174, 2176, 2672, 2673, 2974, 2975, 3611, 3611, 3994, 3994, 4792, 4793, 5267, 5268, 6249, 6249, 6827, 6827, 8026, 8028, 8729

Offset: 1

Author

N. J. A. Sloane, Oct 23 2015

Keywords

• nonn
• base

Links

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

Crossrefs

Partial sums of A263618.

Cf. A002778, A002779, A263616, A263617, A263620.

Programs

Mathematica

Table[Length[Select[Range[0, Floor[Sqrt[10^n]]], PalindromeQ[#^2] &]], {n, 10}] (* 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 A263618 from Chai Wah Wu, Jun 14 2024

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