[seqfan] Lexicographically earliest sequences (need to say "infinite")

Neil Sloane njasloane at gmail.com
Sat Sep 28 20:25:08 CEST 2019


Dear Sequence Fans.
The lexicographic ordering of sequences with distinct positive terms is:
[empty sequence]
[1]
[1,2]
[1,2,3]
...
[2]
[2,1],
etc

Here is an example picked at random where this matters:
A304360 2, 4, 5, 8, 10, 13, 16, 17, ...
Lexicographically earliest sequence of numbers m > 1 with the property
that none of the prime indices of m are in the sequence.

Not true! [2] is earlier than [2, 4, 5, 8, 10, 13, ...]

The definition should say "infinite", thus:
Lexicographically earliest *infinite* sequence of numbers m > 1 with the
property that none of the prime indices of m are in the sequence.

This is not a really serious error, but please keep it in mind when
submitting new sequences.

Neil



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