Enter a numerical palindrome (sequence of positive natural numbers separated by spaces)
Receive the polynomial that gives all possible n ∈ N such that the continued fraction of √n starts with [z, «palindrome», 2z] for some z
«Your polynomial will display here»
How to use this calculator
 Choose a palindrome (ex.: "3 4 1 4 3" or "2 13 13 2")

If it has even length
 Enter the first half (2 13 13 2)
 Leave "Middle element" blank

If it has odd length
 Enter the elements before the middle (3 4 1 4 3)
 Enter the middle element (3 4 1 4 3)
 Click Calculate to get the polynomial
How polynomials are calculated
Palindrome to polynomial mapping:
Palindrome  Polynomial  
[ ] (Empty)  f(x) = x^{2} + 1  x ∈ N 
[2m]  f(x) = (m^{2}x + 1)x  x > 0 
[2m − 1]  f(x) = ((2m − 1)^{2}x + 2)  x > 0 
[1, 2m − 1, 1]  f(x) = ((2m + 1)^{2}x + (2m + 1)^{2} − 2)(x + 1)  x ∈ N 
For the other cases, read the paper