betaprojects

import datetime as dt

delta, c, targetDOW, targetDate = dt.timedelta(days=1), 0, 6, 1
yS, mS, dS,   yE, mE, dE = 1901,1,1,   2000,12,31
yearDelta = yE-yS  # number of years
yS = (yS%400) + 400  # normalized and non-zero

a = dt.datetime(yS, mS, dS)
b = dt.datetime(yS+yearDelta, mE, dE)
while a <= b:

betaprojects

from math import factorial as f
n, m = map(int, input("Enter dimensions (separate by space)?").split())
print ("Routes through a", n, "x", m, "grid", f(n+m) // f(n) // f(m))

betaprojects

def sumn(n, d):  # Sum natural numbers ≤ n that are divisible by d
    n //= d
    return d*n*(n+1) // 2
L = int(input('Enter an upper bound? '))
a, b = 3, 5
s = sumn(L-1, a) + sumn(L-1, b) - sumn(L-1, a*b)
print ("Sum of multiples of", a, "or", b, "below", L, "=", s)

betaprojects

s, x, y = 0, 0, 2
L = int(input('Sum of even Fibonacci numbers <'))
while y < L:
    s, x, y = s+y, y, 4*y+x
print ("is", s)

betaprojects

from math import gcd
from functools import reduce
def LCM(a, b): 
    return a // gcd(a, b) * b
N = int(input("The LCM for numbers 1 through "))
print ("is", reduce(LCM, range(N//2+1, N+1)))

betaprojects

def is_palindromic(n): n=str(n); return n==n[::-1]

dd = dict()
for i in range(101, 1000):
    for j in range(121, 1000, (1 if i%11==0 else 11)):
        p = i*j
        if p >= 101101 and is_palindromic(p): dd[p]=1
lst = sorted(list(dd), reverse=True)
K = int(input("Enter a number between 101101 and 999999? "))
q =  min(lst, key=lambda x:x>=K)

betaprojects

n = int(input('The largest prime factor of '))
while n%2==0: n//= 2  # Remove all even factors
d = 3
while d*d <= n:
    if n % d == 0:
        n//= d
    else:
        d+= 2
print ("is", 2 if n==1 else n)

betaprojects

q = [9*(x+1) * pow(10, x) for x in range(20)]
def d(n):  # find the digit at position n in Champernowne's constant 
    i = 0
    while n>q[i]: n-= q[i]; i+= 1
    L, d = divmod((n-1), i+1)
    return int(str(pow(10, i)+L)[d])
n = input("Enter some indexes, separated by a space? ")
m = 1
for ci in map(int, n.split()):
    m*= d(ci)

betaprojects

prime_sieve()

<def prime_sieve(n):
    sieve = [True] * (n//2)
    for i in range(3,int(n**0.5)+1,2):
        if sieve[i//2]:
            sieve[i*i//2::i] = [False] * ((n-i*i-1)//(2*i)+1)
    return [2] + [2*i+1 for i in range(1,n//2) if sieve[i]]

betaprojects

# -*- coding: utf-8 -*-
n = int(input('first n natural numbers, n ='))
print ("Difference: (Σn)² - Σn² =", n*(n-1)*(n+1)*(3*n+2)//12)