#####
# 1 - HARMONIE
#####
def coma1(g = 4*pi):
    RR = RealField(1000)
    g = RR(g)
    s = 0;
    i = 1;
    while True:
        s = s + RR(1/i)
        if (s > g):
            return i
        i = i + 1
#####
# 2 - GEMENE VEELVOUDEN
#####
def coma2(n = 2^22):
    a = 0;
    logn = log(RDF(n))
    for k in prime_range(2,n+1):
        a += floor(logn/log(RDF(k)))
    return a
#####
# 3 - IS ER MEER TE ZIEN DAN BLABLA
#####
def coma3(n = 5040302010):
    return (fibonacci((n-1) % 46)-1) % 139
# alternatief
def coma2b(m = 139, n=5040302010):
    sqrt5 = sqrt(Mod(5,m))
    phi = (1+sqrt5)/2
    return ((phi-1)^(n+1)*(1+phi) - (-phi)^(n+1)*(2-phi))/sqrt5 - 1
#####
# 4 - SCHEVE TOREN
#####
def coma4(k = 49):
    RR = RealField(300)
    # voldoende bits om k^k * log(k)
    # tot op 5 decimalen te berekenen
    logx = RR(k)^k*log(RR(k))
    return floor(exp(logx - (floor(logx/log(10))-4)*RR(log(10))))
#####
# 5 - PUNTEN TELLEN
#####
def coma5_tel_punten(p):
    n = 0;
    for x in range(0,p):
        for y in range(0,p):
            if (Mod(7*x^3 - 5*x + 2 - 2*y^2, p).is_zero()):
                n += 1
    return n
def coma5(B = 100):
    L = list()
    for p in prime_range(B):
        if (coma5_tel_punten(p) == p):
            L.append(p)
    return L
#####
# 6 - SPOORZOEKEN
#####
def coma6(g = 2010):
    # (enkel voor g%2 == 0)
    RR = RealField(50)
    S = RR(0);
    for i in range(1,g+1):
        S = S + 1/i
    return RR(1+S/g)

print coma1()
print coma2()
print coma3()
print coma4()
print coma5()
print coma6()