Hello Math-Fun (this is an attempt to send a message to the mailing list via my new gmail address I've subscribed in order to avoid warning messages that people sometimes get from me; the hereunder message will be more readableif you click this link: http://cinquantesignes.blogspot.com/2020/07/1-spiral-10-diagonals-1-sequence... )
Pick any digit zero and start a clockwise spiral on this infinite square lattice (streaked by the same succession of ten different diagonals, one digit per square); the resulting sequence *S* is the lexicographically earliest of distinct positive terms:
012569874301256987430125698743012569874301256987430125698743 125698743012569874301256987430125698743012569874301256987430 256987430125698743012569874301256987430125698743012569874301 569874301256987430125698743012569874301256987430125698743012 698743012569874301256987430125698743012569874301256987430125 987430125698743012569874301*2**5*6987430125698743012569874301256 874301256987430125698743012*569874301*256987430125698743012569 743012569874301256987430125*698743012*569874301256987430125698 430125698743012569874301256*987430125*698743012569874301256987 301256987430125698743012569*8743**0**1256*987430125698743012569873 012569874301256987430125698*74301*2*569*874301256987430125698743 125698743012569874301256987*430125698*743012569874301256987430 256987430125698743012569874*301256987*430125698743012569874301 569874301256987430125698743*012569874*301256987430125698743012 698743012569874301256987430125698743012569874301256987430125 987430125698743012569874301256987430125698743012569874301256 874301256987430125698743012569874301256987430125698743012569 743012569874301256987430125698743012569874301256987430125698 430125698743012569874301256987430125698743012569874301256987 301256987430125698743012569874301256987430125698743012569873 ... *S* = *0*, *1*, *2*, *10*, *3*, *4*, *30*, *12*, *5*, *6*, *52*, *103*, *47* , *8*, *7*, *430*, *125*, *69*, *89*, *65*, *210*, *34*, *78*, *9*, *698*, *74*, *301*, *25*, *6987*, *478*, *96*, *5210*, *347*, *896*, *525*, ... Any other order of the ten diagonals will not produce a lexicographically earliest sequence of distinct positive terms (I guess). Best, É.