A090748=A000043.apply(lambda n:n-1,desc='Numbers n such that 2^(n+1) - 1 is prime.')
A006862=Sequence(
math2.euclid_gen,
# lambda n:math2.mul(math2.primes(n))+1, # TODO: make it faster
desc="Euclid numbers: 1 + product of the first n primes."
)
A002110=A006862-1
A002110.desc="Primorial numbers (first definition): product of first n primes"
A057588=(A002110-1).filter(bool) #remove leading 0 ...
A057588.desc="Kummer numbers: -1 + product of first n consecutive primes."
A005234=A000040.filter(
lambda n:math2.is_prime(math2.mul(math2.sieve(n+1))+1), #TODO: find a simple way to reuse A006862 or euclid_gen
desc='Primorial primes: primes p such that 1 + product of primes up to p is prime'
)
A034386=Sequence(
0,
lambda n:math2.mul(math2.sieve(n+1,oneisprime=True)),
desc="Primorial numbers (second definition): n# = product of primes <= n"
)
#TODO: understand why A000720 creates a hudge bad side effect on many other serquences
"""
A000720=Sequence(
1,
lambda n:len(math2.sieve(n+1,oneisprime=True)),
A090748=A000043.apply(lambda n:n-1,desc='Numbers n such that 2^(n+1) - 1 is prime.')
A006862=Sequence(
math2.euclid_gen,
# lambda n:math2.mul(math2.primes(n))+1, # TODO: make it faster
desc="Euclid numbers: 1 + product of the first n primes."
)
A002110=A006862-1
A002110.desc="Primorial numbers (first definition): product of first n primes"
A057588=(A002110-1).filter(bool) #remove leading 0 ...
A057588.desc="Kummer numbers: -1 + product of first n consecutive primes."
A005234=A000040.filter(
lambda n:math2.is_prime(math2.mul(math2.sieve(n+1))+1), #TODO: find a simple way to reuse A006862 or euclid_gen
desc='Primorial primes: primes p such that 1 + product of primes up to p is prime'
)
A034386=Sequence(
0,
lambda n:math2.mul(math2.sieve(n+1,oneisprime=True)),
desc="Primorial numbers (second definition): n# = product of primes <= n"
)
#TODO: understand why A000720 creates a hudge bad side effect on myna other serquences
"""
A000720=Sequence(
1,
lambda n:len(math2.sieve(n+1,oneisprime=True)),
def npixels(self):
return math2.mul(self.size)
def npixels(self):
return math2.mul(self.size)
