interator 0.1

Integer sequence generation and related conditional tests.

interator

Module for integer sequence generation and related conditional tests.

Contents

Fibonacci Sequence

Function	Description
fibonacci_stream(start = (0,1))	Yield the next Fibonacci number starting with F(0)
negafibonacci_stream(start = (0,1))	Yield the next Fibonacci number in the negative index starting with F(0)
nth_fibonacci(n, start = (0, 1))	Given an index n, find F(n)
lucas_stream(P = 2, Q = -1, start = (0, 1))	Yield the next number in the in the (P,−Q)-Lucas sequence starting with U0(P,Q)
is_fibonacci(n, start=(0,1))	Determine if n is within the Fibonacci sequence
is_lucas(n, P = 2, Q = -1, start = (0, 1))	Determine if n is within the (P,−Q)-Lucas sequence

Generalizations

By default, fibonacci_stream, negafibonacci_stream, nth_fibonacci, and is_fibonacci work with the Fibonacci numbers, and lucas_stream and is_lucas work with the Pell numbers. However, by changing start, any generalization of these sequences can be generated. Here are some common examples:

import interator

stop = 10
numbers = {'Lucas' : (2, 1),
           'Tribonacci' : (0, 0, 1),
           'Tetranacci' : (0, 0, 0, 1)}


for name, start in numbers.items():
    print('%s numbers:' % name)
    for i, n in enumerate(interator.fibonacci_stream(start=start)):
        print(n, end = ' ')
        if i == stop:
            print('\n')
            break

Please note the Lucas numbers should not be confused with the Lucas sequence. The Lucas numbers are a specific example of the Lucas sequence.

Prime Numbers

Functions	Description
prime_stream()	Yield the next prime number starting with 2
composite_stream()	Yield the next composite number starting with 1
is_prime()	Test the primality of n by checking potential prime factors
miller_rabin(n, k = 8)	Perform the Miller-Rabin Primality Test on n
is_composite(n)	Test if n is a composite number by checking potential prime factors

Polygonal Numbers

Functions	Description
polygonal_stream	Yield the next s-gonal number starting with 1
is_polygonal(n, s)	Test if n is an s-gonal number

Licensing

This project is licensed under the MIT License.