[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):


Franklin T. Adams-Watters

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


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

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.

1, 2, 3, 4, 6, 19, 23, 25, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 
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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