tkmharris

{-- Implementation of the Akiyama-Tanigawa algorithm
	for computing Bernoulli numbers. --}

{-- Implement the algorithm by:
	1. Begin with list of reciprocals of positive integers.
	2. Write function to get next row and iteratie it to get list of lists.
	3. Take the head of each list in the list to get Bernoulli nums.
	Everything evaluates lazily, so we can do this nicely with infinite lists. 

	See tkmh.space/flotsam/haskell-akiyama-tanigawa for more.--}

tkmharris

{--
We provide a function 'nextPrimeBias' that when called as
  nextPrimeBias a b n r
returns the probability that, among the first r primes, a prime that is equivalent to a mod n is followed by a prime that is equivalent to b mod n.

We see that these probabilities are not evenly distributed among equivalence classes, as described in https://arxiv.org/abs/1603.03720 :
nextPrimeBias 7 1 10 100000 = 0.25736558
nextPrimeBias 7 3 10 100000 = 0.27695382
nextPrimeBias 7 7 10 100000 = 0.144993
nextPrimeBias 7 9 10 100000 = 0.3206876

tkmharris

## Mordell's equation

'''
Get integer solutions of the Mordell equation
y^2 = x^3 - d
for certain special values of d.
See mordell.txt for details.
'''

def mordell_test(d, x,y):

tkmharris

def hurwitz_radon(n):
    '''Takes a positve integer n; returns the Hurwitz-Radon number p(n).
    p(n) defined as follows:
    Let n = (2^v)m with m odd and write v = 4a + b, 0<= b < 4.
    Then p(n) = 8a + 2^b.'''
    if not isinstance(n, int):
        raise TypeError("hurwitz_radon only defined for positive integers")
    if n <= 0:
        raise ValueError("hurwitz_radon only defined for positive integers")
    # helper to get largest power of 2 divinding n