Parity of p(p+1)/2 for nth prime p

[Richard Guy]

Where angels fear to tread ...

Surely this must be the Law of Small Numbers?

I only checked a few values --- how far has
it been checked?  More terms are easily
calculated by almost anyone but me.  Perhaps
someone has already gone far enough ... ?

[just a faint chance that A034933 = A082749
mod 2  is true ?]   R.

On Fri, 10 Sep 2004, JEREMY GARDINER wrote:

>
> The following sequences (allowing offset of first term) all appear to have the same parity:
>
> A034953 Triangular numbers with prime indices
> A054269 Length of period of continued fraction for sqrt(p), p prime
> A082749 Difference between the sum of next prime(n) natural numbers and the sum of next n primes
> A006254 Numbers n such that 2n-1 is prime
> A067076 2n+3 is a prime
>
> Jeremy Gardiner
>