The number [tex](a+1)^{n}) - a^{n}[/tex] (where a is any positive integer, and n > 1 is prime number), if not being prime,

has as its divisor(s)/factor(s) the member(s) of arithmetic progression with step 2n.

n = 3 -> {7,13,19,25,31,37,43,49,55,61,67,73,…}

n = 5 -> {11,21,31,41,51,61,71,81,91,101,…}

n = 7 -> {15,29,43,57,71,85,99,113,127…}

n = 11 -> {23,45,67,89,111,133,155…}

and so on …..

Programmatically (I used a JavaScript code) this discovery was proved for different range of numbers a and n.