Are the stable homotopy groups $\pi^s\_i(\mathbb R P^{\infty})$ known for small $i$? In particular, I would be interested in the values for $i = 5,6$. A quick Internet search did not lead to anything.



Stable homotopy groups of $RP^{\infty}$
The following paper contains a list of stable homotopy of projective spaces in dimensions $\leq 8$:


* A. Liulevicius. A theorem in homological algebra and stable homotopy projective spaces. Transactions of the American Mathematical Society
Vol. 109, No. 3 (Dec., 1963), pp. 540-552


[JSTOR link](http://www.jstor.org/stable/1993859)


In particular, $\pi^s\_5=0$ and $\pi^s\_6=\mathbb{Z}/2$.


