48th Austrian Mathematical Olympiad

Dora can ignore Claire's numbers, since Anthony has already written them all. Considering the numbers up to $3000$ we see that Anthony has already written down $1500$ of them and Bertha has written $1000$ of them, $500$ of which have been written twice, which are ignored by Dora in their second occurrence. Hence Dora denotes exactly $2000$ numbers up to $3000$. The next $17$ numbers written by Dora are $3002$, $3003$, $3004$, $3006$, $3008$, $3009$, $3010$, $3012$, $3014$, $3015$, $3016$, $3018$, $3020$, $3021$, $3022$, $3024$, $3026$. Thus $3026$ is the $2017$th number on Dora's list.