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i = 2
n_0 = 4

while True==True:
    v_2 = (float(1)/float((i*4)-3))
    v_3 = (float(1)/float((i*4)-5))
    n_1 = float(n_0) + (4 * (v_2 - v_3))
    n_0 = float(n_1)
    i+=1
    print(n_1)

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####TESTING######
'''
CRYPTO PROOFS
'''
    
'''
def SUB_PROOF(sub_set,theta_input):
    #This function is checking if each index location contained in subset is either
    #a set of 1's or 0's in theta's input.
    to_check=[]

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def keccak_(ip):
    for i in range(24):
        ip=iota(chi(pi(rho(theta(ip)))),i)
    return(ip)
    
 zero=['1100110001001101000111100111110100011100011110010010000000111110',
      '0110101100110010001101101000110101010000010100110101111110010011',
      '1001011100010011110100011100111000001010100011111011001010001101',
      '0000010001110000101100000100101001111011011000011110000101001101',

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from Tkinter import *

class MyFirstGUI:
    def __init__(self, master):
        self.master = master
        master.title("Calculator")
        global TEXT_VALUE
        global TEXT_BOX
        global GENERAL_PRECISION
        global SPECIFIC_PRECISION

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def to_print(object):
    for i in range(len(object)):
        print(object[i])

def l_s(bit_list):
    bit_string=''
    for i in range(len(bit_list)):
        bit_string+=bit_list[i]
    return(bit_string)

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#https://gist.github.com/back-seat-driver/b2f81929741cd94b1ff17086fdaad0bd

def bin_n_bit(dec,n):
    return(str(format(dec,'0'+n+'b')))

def hex_n_bit(dec,n):
    return(str(format(dec,'0'+n+'x')))

def xo_set(ip_0,ip_1):
    to_return=[]

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from Tkinter import *
import csv
import win32clipboard
import os

def bat_exe():
    '''
    Note that both methods will execute a batch file from your home directory.
    '''
    #os.system("F:/Anaconda3/pdm_open.bat")

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def conversion(str_list):
    for i in range(len(str_list)):
        str_list[i]=int(str_list[i])
    return(str_list)

def trim_end(a_string):
    return(a_string[0:len(a_string)-1])

def dec_shift(a_string):
    to_build_0=''

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def bin_theta(ip):
    c_xz=[]
    for i in range(5):
        c_xz.append(ip[i] ^ ip[i+5] ^ ip[i+10] ^ ip[i+15] ^ ip[i+20])
    d_xz=[]
    for i in range(5):
        d_xz.append(c_xz[(i-1)%5] ^ rot(c_xz[(i+1)%5],1,64))
    for i in range(5):
        ip[i]    = ip[i]    ^ d_xz[i]
        ip[i+5]  = ip[i+5]  ^ d_xz[i]

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def bin_n_bit(dec,n):
    return(str(format(dec,'0'+n+'b')))

def hex_n_bit(dec,n):
    return(str(format(dec,'0'+n+'x')))

def xo_set(ip_0,ip_1):
    to_return=[]
    for i in range(len(ip_0)):
        to_return.append(ip_0[i] ^ ip_1[i])