

A260139


For any term a(k), there are exactly a(k) terms strictly smaller than 3*a(k); this is the lexicographically first increasing sequence of nonnegative integers with this property.


2



0, 2, 6, 7, 8, 9, 18, 21, 24, 27, 28, 29, 30, 31, 32, 33, 34, 35, 54, 55, 56, 63, 64, 65, 72, 73, 74, 81, 84, 87, 90, 93, 96, 99, 102, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 162, 165, 168, 169, 170, 171, 172
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OFFSET

0,2


COMMENTS

Suggested by Eric Angelini, cf. link to SeqFan post.
This sequence has a nice selfsimilar 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[k1]+1))


CROSSREFS

Cf. A260107, A130011 and references therein; A037988, A094591 (analogs with 2n instead of 3n).
Sequence in context: A047279 A162917 A250183 * A118471 A167456 A023633
Adjacent sequences: A260136 A260137 A260138 * A260140 A260141 A260142


KEYWORD

nonn,easy,look


AUTHOR

M. F. Hasler, Jul 16 2015


STATUS

approved



