noodling/palindromes.py

# 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?

from math import *

def half(x):
    return ceil(float(x)/2)

def pals(n, b):
    return (b-1)*(b**(half(n-1)))

def num(n, b):
    return (b-1)*(b**(n-1))

def prop (n, b):
    return pals(n, b)/num(n, b)

def testex(nm, bm):
    if (nm==2 & bm==1):
        return ""
    elif (bm==1):
        return ""
    elif(nm==2):
        return ""
    else:
        return (str(nm)+" digits in base "+str(bm)+" gives "+
                str(floor(prop(nm,bm)*100))+" percent palindromes. "+
                test(nm-1,bm)+test(nm,bm-1))

def test(nm, b):
    if(nm==2):
        return ""
    else:
        return(str(nm)+" digits: "+str(prop(nm,b)*100)+" percent palindromes. "
                +test(nm-1,b))