Does anybody have any ideas how to solve the equation $x=\phi(x)+\phi(x+1)-1$, where $x$ is a natural number and $\phi$ is Euler's totient function?


I failed even to figure out whether this equation has finite number of solutions or infinite.


Any help will be appreciated.



Equation $x=\phi(x)+\phi(x+1)-1$
This is [OEIS Sequence A067798](https://oeis.org/A067798).
Nothing else seems to be known about it; at any rate OEIS gives no
references to the literature, only a link to 
[a list of further such $x$](https://oeis.org/A067798/b067798.txt)
 from Giovanni Resta that extends it from the 43rd solution, $722015$, 
to the 76th, $1103806594815$, which is just a a bit larger than $2^{40}$.
(Thanks to **Robert Israel** for noting this link in his comment.)


It seems very hard to do anything with the problem other than make a few
elementary observations (e.g. all $x>2$ will be odd), do some heuristics
(biases mod $3$, $4$, $5$, and other small moduli; expected asymptotics),
and use yet more computing power to find a handful of further solutions.


