Thank you. I'll have to look up Calkin–Wilf tree and Stern's Diatomic Sequence.

(adding that they are talking about java)
and to answer the question, yes.
inital code (returning empty string) results in test output:

expected:<[]> but was:<[L)exJmASs1D?qCGTPzh.cj7XM1m/qC{Q=4gb%k<igJE.^jWQn!ux[h~R[2r@OC$SH)gbwnCu%2D?9N|Q:4>x$khdQJB%rvgShwh.vnjdG35+&6KU|1IbMmhdG3r@}@gSD2`EwnCu[2T*.Y$S97J.;m"iAJT<eC{Q0tobWo?zs1G?[*WQSz^a;mgM;I2+!6ASp!!xToJB[26=nvgSQz*ELmJB$JQ*m6gSM)VEcjqMwJ]>

Bonus issue:
s/charakters/characters

Thanks

simple is the best