Marinada '19

Neka je \(a_1 = \dfrac{1+ \sqrt{5}}{2}\), \(b_1 = 0\), \(b_{n+1} = 2b_n+1\) te \(a_{n+1} = a_1a_2\ldots a_n + (a_1+1)^{b_n}\). Ako \(\left\lceil x \right\rceil\) označava najmanji cijeli broj koji nije manji od \(x\), odredi: \[\left\lceil \log_2 \left\lceil \dfrac{\ln{(\left\lceil a_{2019} \right\rceil - a_{2019})}}{\ln{(\sqrt{5}-1)} - \ln{2}} \right\rceil \right\rceil \ (\mathrm{mod}\ 41)\]