[seqfan] Recaman observation

[David Wilson]

Recaman's sequence is defined as

a(n) =

	0, if n = 0

	a(n-1)-n if n > 0, a(n-1)-n >= 0 and a(n-1)-n not already in sequence.

	a(n-1)+n otherwise

So Recaman satisfies

[1] a(n) >= 0
[2] |a(n)-a(n-1)| = n

and tries to avoid repeats by greedy choice of a(n) = a(n-1) -+ n.

Recaman also "wants" to be an injection on N = {0, 1, 2, ...}, as it 
attempts to avoid repeats by choice of a(n) = a(n-1) + n when a(n) = 
a(n-1) - n is a repeat.

Clearly, there are injections satisfying [1] and [2], e.g, a(n) = n(n+1)/2.

Is there a lexicographically smallest injection satisfying [1] and [2]?