A112530: p(n)+/ n and p(n)+/-2n are all primes.

[Ralf Stephan]

zak wrote 
> Just submitted A112530:
> Numbers n such that prime(n) +/- n and prime(n) +/- 2n
> are all primes
> 720,1920,5580,14370,17160,21090,26040,28560,...
> Why are all n's  divisible by 30?

Because you have 5 primes in an arithmetic progression,
and if the exponent of 2, 3 or 5 in the distance was
zero, some of the 5 would be divisible by 2, 3 or 5.

Extend it to 7 primes --> you need 7 as factor too = 210.
This has nothing to do with n being parameter to the prime()
function, that makes only that you get a subset of all solutions.


ralf