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

Richard Guy rkg at
Fri Sep 10 19:20:40 CEST 2004

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

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