[seqfan] seqs whose |differences| are 1,2,3,4,...

[N. J. A. Sloane]

Dear Seqfans,

Consider all rearrangements of the natural numbers with the property that
the absolute values of the differences are 1,2,3,4,5,... (in that order).

John Conway asks, what is the lexicographically earliest such sequence?

The greedy approach leads you to A078943, which dies after 24 terms.

Recaman's sequence A005132 (or rather, the version defined
on the positive integers, A063733) is another failure, because it contains
repeated terms.

Does anyone have a candidate for the answer?

Neil