You found a strong, long rope! All of you manage to pass the bridge by tying one end of it firmly to a strong boulder, the other to your waist. However, now that all are safe, your mind wanders into the realms of the abstract. Given the dimensions of the rope, wouldn't it be more efficient to have more than 1 person cross the bridge at once? What could be the maximum number of people you could shove into a tight-knot so that no casualties occur? Bipradeep joins in your musings, and you strike up a conversation.

Do there exist increasing arithmetic progressions with positive integer terms, where each of these sequences do not contain any term of the Fibonacci sequence?

If you think that there aren't any, your answer should be no. Otherwise, find those sequences among these which have the least possible common difference; among these, pick that sequence with the least possible first term. Concatenate the first five terms of this sequence as your answer. For example, if you think that the sequence starts off with $2$, $4$, $6$, $8$, $10$, ..., then your answer should be $246810$.