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A128921

Palindromes m such that reverse of m^2 is also a square.

0, 1, 2, 3, 11, 22, 33, 99, 101, 111, 121, 202, 212, 1001, 1111, 2002, 10001, 10101, 10201, 11011, 11111, 11211, 20002, 20102, 100001, 101101, 110011, 111111, 200002, 1000001, 1001001, 1002001, 1010101, 1011101, 1012101, 1100011, 1101011

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OFFSET

1,3

COMMENTS

Most terms have a palindromic square; for the rare exceptions see A133901. - Klaus Brockhaus and Zak Seidov, Sep 29 2007

LINKS

Klaus Brockhaus, Table of n, a(n) for n = 1..360

EXAMPLE

33 and 99 are terms because 33^2=1089 => 9801=99^2 and 99^2=9801 => 1089=33^2.

MATHEMATICA

A128921=Select[Range[0, 100000], IntegerQ[Sqrt[FromDigits[Reverse[IntegerDigits[ #^2 ]]]]]&&FromDigits[Reverse[IntegerDigits[ # ]]]==#&]

Select[Range[0, 1110000], PalindromeQ[#]&&IntegerQ[Sqrt[IntegerReverse[#^2]]]&] (* Harvey P. Dale, Feb 09 2026 *)

PROG

(Python)

from sympy.ntheory.primetest import is_square

from itertools import chain, count, islice

def A128921_gen(): # generator of terms

return filter(lambda n:is_square(int(str(n**2)[::-1])), chain((0, ), chain.from_iterable(chain((int((s:=str(d))+s[-2::-1]) for d in range(10**l, 10**(l+1))), (int((s:=str(d))+s[::-1]) for d in range(10**l, 10**(l+1)))) for l in count(0))))

A128921_list = list(islice(A128921_gen(), 20)) # Chai Wah Wu, Jun 23 2022

CROSSREFS

Cf. A002113, A057135, A057136, A133901.

Sequence in context: A316187 A215952 A276375 * A118595 A229549 A229804

Adjacent sequences: A128918 A128919 A128920 * A128922 A128923 A128924

KEYWORD

nonn,base,easy

AUTHOR

Zak Seidov, Mar 02 2005, definition corrected Sep 16 2007

EXTENSIONS

More terms from Klaus Brockhaus, Sep 23 2007

STATUS

approved

URL: https://oeis.org/A128921

⇱ A128921 - OEIS