Tuesday, January 18, 2011

Sum and Difference of Two Cubes

http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Broughan/broughan25.pdf

Differences between two positive cubes in exactly 1 way

Differences between two positive cubes in exactly 2 ways

Differences between two positive cubes in exactly 3 ways

Difference between two positive cubes in more than one way

Differences between positive cubes in 1, 2 or 3 ways:
union of A014439, A014440 and A014441

Numbers n such that n and n+1 are differences between 2 positive cubes
in at least one way

Numbers n such that n and n-1 are differences between 2 positive cubes
in at least one way

Numbers n such that n is a perfect square and is a difference
between 2 positive cubes in at least one way

Numbers n such that n^2 is a difference between 2 positive cubes
in at least one way

Differences between numbers that are a difference between 2 positive cubes
in at least one way

Numbers n such that n-th and (n+1)st term of A038593 differ by 1

Numbers that are not the difference between two positive cubes

Palindromic numbers which are the difference of two positive cubes

Odd numbers that are differences between two cubes in at least one way

Even numbers that are differences between two cubes in at least one way

Numbers that are divisible by 4 and are differences between two cubes
in at least one way

Numbers that are divisible by 8 and are differences between two cubes
in at least one way

Divisible by 3 (and 9) and are differences between two cubes in at least one way

Numbers that are divisible by 6 (and 18) and are differences between two cubes
in at least one way

Numbers that are divisible by 5 and are the difference between two
(different positive) cubes in at least one way

Numbers that are divisible by 10 and are differences between two cubes
in at least one way

Numbers that are divisible by 7 and are differences between two cubes
in at least one way

Numbers n such that n ends with '1' and is difference between two cubes
in at least one way

Numbers n such that n ends with '2' and is difference between two cubes
in at least one way

Numbers n such that n ends with '3' and is difference between two cubes
in at least one way

Numbers n such that n ends with '4' and is difference between two cubes
in at least one way

Numbers that end in '5' and are the difference between two (positive) cubes
in at least one way

Numbers n such that n ends with '6' and is difference between two cubes
in at least one way

Numbers n such that n ends with '7' and is the difference between two cubes
in at least one way

Numbers n such that n ends with '8' and is difference between two cubes
in at least one way

Numbers n such that n ends with '9' and is difference between two cubes
in at least one way

Numbers whose square is expressible as the difference of positive cubes
in more than one way

Semiprimes that can be expressed as the sum or difference of two cubes.
Common terms of A001358 and A045980

a(n) = 15n^2 + 13n^3

Positive sums or differences of two cubes of primes

Smallest number that is the difference between two positive cubes in n ways

Numbers expressible as sum or difference of two cubes of primes
in at least two ways

Triangular numbers which are differences of nonnegative cubes

(n) = number of solutions to x^3 - y^3 == 0 (mod n)

Numbers of the form x^3 + y^3 or x^3 - y^3
Product of three solutions of the Diophantine equation x^3 - y^3 = z^2
Numbers expressible as the difference of two nonnegative cubes

Sequence and first differences (A030124) include all numbers exactly once

Complement (and also first differences) of Hofstadter's sequence A005228