Package de.tilman_neumann.jml

Class SumOf4Squares

java.lang.Object

de.tilman_neumann.jml.SumOf4Squares

public class SumOf4Squares
extends Object

Stuff concerning sums of 4 squares representations of natural numbers.

Author:

Tilman Neumann

Constructor Summary

Constructors

Constructor	Description
SumOf4Squares()

Method Summary

Modifier and Type	Method	Description
static TreeSet<Long>	getA004215(long m)	Compute all elements of A004215 below m, i.e.
static TreeSet<Long>	getA004215_v2(int n)	Compute all elements of A004215 below m = 2^n, i.e.
static int	getA004215_v3(int n, long[] array)	Another implementation using arrays, much faster than the previous ones.
static void	main(String[] args)	A test of the hypothesis that A023105(2^n) == 2 + the number of entries of A004215 that are less than 2^n, for n>0.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

SumOf4Squares

public SumOf4Squares()

Method Detail

getA004215

public static TreeSet<Long> getA004215(long m)

Compute all elements of A004215 below m, i.e. all k= 0, j >= 0.

Parameters:

m -

Returns:

A004215 entries < m

getA004215_v2

public static TreeSet<Long> getA004215_v2(int n)

Compute all elements of A004215 below m = 2^n, i.e. all k

Parameters:

n -

Returns:

A004215 entries < 2^n

getA004215_v3

public static int getA004215_v3(int n,
                                long[] array)

Another implementation using arrays, much faster than the previous ones.

Parameters:

n - such that m=2^n

array - an array big enough to take roughly 2^n/6 values

Returns:

number of entries

main

public static void main(String[] args)

A test of the hypothesis that A023105(2^n) == 2 + the number of entries of A004215 that are less than 2^n, for n>0. Confirmed until n=29.

Parameters:

args - ignored