Can you provide a counterexample to the claim given below ?
Inspired by Euler's conjecture about $8n+3$ (see page 4 of this note ) I have formulated the following claim :
For any nonnegative integer $n$ , $8n+6$ can be represented as a sum : $$8n+6 = a^2 +2p$$ , where $a$ is a nonnegative integer , and $p$ is a prime .
I have tested this claim for all $n$ up to $2 \cdot 10^6 $ .