# [seqfan] Re: minima of certain sets(recursive)

franktaw at netscape.net franktaw at netscape.net
Mon Jan 18 16:15:40 CET 2010

```In other words, a(n) is the smallest positive integer not occurring
previously in the sequence, and not representable as 2x+3y where x and
y are in the sequence.

To answer your question literally, you can calculate the sequence up to
the point where either the number in question appears or a larger one
appears; in the former case, it is in the sequence, and in the latter,
it is  not.

That may seem a bit facetious, but really it isn't.  The chances are
that there is no significantly simpler method of determining membership
in this sequence.  The almost-but-not-quite regular behavior typically
means that no such simplification is possible.

You might also want to look at the same definition, except with domain
non-negative integers instead of positive integers.  This sequence
starts (hand calculated):

0,1,4,6,7,9,10,13,...

-----Original Message-----
From: Tobias Friedrich <Tobias.Friedrich at stmail.uni-bayreuth.de>

Hello,

How can you decide if a number occurs in this sequence?

M_0={}
a_n=min(N\( {2x_1+3x_2| x_1,x_2 in M_{n-1}} u M_{n-1} ))
M_n=M_{n-1} u {a_n}

Sorry for my bad formating.
This file include formulas and some diagrams. You can see that there
are some
"steps" in the sequnce.
http://tobispace.to.funpic.de/folge.pdf

Sequence:
1, 2, 3, 4, 6, 19, 23, 25, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38,
39,
40,...
http://tobispace.to.funpic.de/fach.txt (Sequence to  49999792)

Moreover you can make generalizations, i.e. you can change the
coefficients 2,3
or you can change the number of variables x_1,x_2,x_3,...

But this example is the simplest non trivial example.

Sincerely yours,

Tobias Friedrichy yours,

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```