A263616 -id:A263616 - cp's OEIS frontend

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

N. J. A. Sloane, Oct 23 2015

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

Partial sums of A263616.

Cf. A002778, A002779, A263618, A263619.

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

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

A263619 Number of palindromic squares with at most n digits.

Original entry on oeis.org

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

N. J. A. Sloane, Oct 23 2015

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

Partial sums of A263618.

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

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

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

cp's OEIS Frontend

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

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