noodling/palindromes.hs

-- Author: estelendur
-- Given a base b and a number of digits n, how many palindromic integers?
-- What proportion of possible integers are palindromes?
-- Can we learn anything interesting from this?

--half :: (Integral a) => a -> a
--half x = ceiling(x/2)

--pals :: (Integral a) => a -> a -> a
pals n b = (b-1)*(b^(ceiling((n-1)/2))

--num :: (Integral a) => a -> a -> a
num n b = (b-1)*(b^(n-1))

prop :: (Integral a) => a -> a -> Double
prop n b = (pals n b)/(num n b)

-- Find out the proportion of palindromes for all n, b up to nm, bm
test :: (Integral a) => a -> a -> String
test 1 1 = "1 digit in base 1 gives 1 palindrome\n"
test n 1 = n ++ " digits in base 1 gives 1 palindrome\n"
test 1 b = "1 digit in base " ++ b ++ " gives " ++ (b-1) ++ " palindromes\n"
test nm bm = nm ++ " digits in base " ++ bm ++ " gives " ++ (prop nm bm)*100 ++ " percent palindromes\n" ++ (test (nm-1) bm) ++ (test nm (bm-1))