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)