[seqfan] Is the definition of this sequence correct?

[Ali Sada]

Hi everyone,

Please check this definition

a(1) =1; a(n) is the lexicographically earliest positive integer such that the distance between a(n) and a(n)+1 is >= a(n) in both directions. (The distance between a(n) and a(m) is |n-m|)

a(1) = 1
a(2) = 2
Now, a(3) cannot be 3, so a(3) = 4.
a(4) cannot be 3 nor 5, so a(4) = 6.
a(5) cannot be 3 nor 5 nor 7, so a(5) = 8.
Now, we can use 3 for a(6) (the distance with 4 is 3).
And so on.

I would appreciate your help with the correct definition and terms. 

Best,

Ali