login
A128921
Palindromes m such that reverse of m^2 is also a square.
4
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
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
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[ # ]]]==#&]
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
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