Is there a pattern for those integers that are palindromes and their squares are also palindromes?
by 
Farino
ANSWERS: 2
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There are some cool patterns within the set of integers that are palindromes and whose squares are palindromes. 11 : 121 101 : 10201 111 : 12321 1001 : 1002001 etc. I don't know if there is a pattern in general, though.
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Here are all of them from 1 digit to 5 digits. Can you see a pattern? 1 1 2 4 3 9 11 121 22 484 101 10201 111 12321 121 14641 202 40804 212 44944 1001 1002001 1111 1234321 2002 4008004 10001 100020001 10101 102030201 10201 104060401 11011 121242121 11111 123454321 11211 125686521 20002 400080004 20102 404090404 and it continues with these numbers: 100001, 101101, 110011, 111111, 200002, 1000001, 1002001, 1010101, 1011101, 1012101, 1100011, 1102011, 1110111 I can see stuff like: you can put zeros in anywhere, as long as they are symmetrical. You can have 1,11,111,etc up to nine ones. The only exceptions to those rules in the list are thse: 2,3,22,121,212,11211 Aparently there is a pattern: it's all those palindromes where the sum of the squares of digits are less than 10. By sheer luck, I've listed every single possibility in the last paragraph.
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