OFFSET
0,2
COMMENTS
Suggested by Eric Angelini, cf. link to SeqFan post.
This sequence has a nice self-similar graph.
LINKS
M. F. Hasler, Table of n, a(n) for n = 0..999
E. Angelini, Re: A130011 and the definition of "slowest increasing"., SeqFan list, July 13, 2015
FORMULA
a(n) <= 3n, with equality for indices of the form n = a(k) for some k.
EXAMPLE
The first term says that there are a(0) = 0 terms < 0.
Then it is not possible to go on with 1, since {0, 1} would be 2 terms < 3*1 = 3.
Thus we must have a(1) = 2 terms < 3*2 = 6; and since we already have {0, 2}, the next must be at least 6.
Therefore, a(2) = 6 is the number of terms < 3*6 = 18, so there must be 3 more:
We have a(3) = 7 terms < 21, a(4) = 8 terms < 24, a(5) = 9 terms < 27.
Now, in view of a(2), the sequence goes on with a(6) = 18 terms < 3*18. This was the 7th term, in view of a(3) the next must be >= 21:
We have a(7) = 21 terms <= 3*21, a(8) = 24 terms <= 3*24, a(9) = 27 terms <= 3*27. Then we can increase by 1 up to index 18:
a(10) = 28 terms <= 3*28, ..., a(17) = 35 terms <= 3*35. This was the 18th term, in view of a(6) the following terms must be >= 3*18 = 54 =: a(18).
PROG
(PARI) a=vector(100); a[i=2]=2; for(k=3, #a, a[k]=if(k>a[i], 3*a[i++-1], a[k-1]+1))
CROSSREFS
KEYWORD
AUTHOR
M. F. Hasler, Jul 16 2015
STATUS
approved