A397142 - OEIS

A397142

Palindromes without digit 0 whose square is also a palindrome.

1, 2, 3, 11, 22, 111, 121, 212, 1111, 11111, 11211, 111111, 1111111, 11111111, 111111111

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OFFSET

1,2

COMMENTS

Theorem: The square of a palindrome P is also a palindrome iff the sum of the squares of the digits of P is less than 10 (see Diophante link).

From this sequence, we obtain the palindromes with digit 0 such that the square is also a palindrome, by adding 0's to each term to obtain new palindromes. For example, from 212, we obtain 20102, 2001002, 200010002, ... .

LINKS

Table of n, a(n) for n=1..15.

Diophante, A317 = Palindromes et leurs carrés palindromes (in French).

EXAMPLE

111111111^2 = 12345678987654321, so 111111111 is a term.

CROSSREFS

Intersection of A057135 and A052382.

Cf. A104075 (subsequence of repdigits).

Sequence in context: A241096 A057135 A229805 * A104075 A383184 A339753

Adjacent sequences: A397139 A397140 A397141 * A397144 A397145 A397146

KEYWORD

nonn,fini,full

AUTHOR

Bernard Schott, Jul 21 2026

STATUS

approved