Sequence: "if n appears then a*n+b doesn't"

[David Wilson]

A121538 is essentially A053661-1.

The binary representations of both A053661 and A121538 form the languages of 
a finite automata. Furthermore, any S which obeys the rule "if n appears 
then an+b does not", or more precisely, "if k is not in S, then k = an+b 
where n is in S" for sufficient n, will have n-ary representations that form 
the language of a finite automaton.

----- Original Message ----- 
From: "Max A." <maxale at gmail.com>
To: "zak seidov" <zakseidov at yahoo.com>
Cc: <seqfan at ext.jussieu.fr>
Sent: Sunday, August 06, 2006 6:40 AM
Subject: Re: Sequence: "if n appears then a*n+b doesn't"


> On 8/6/06, zak seidov <zakseidov at yahoo.com> wrote:
>
>> %S A121538 
>> 1,2,4,6,7,8,10,11,12,14,16,18,19,20,22,24,26,27,28,30,31,32,34,35,36,38,40,42,43,44,46,47,48,50,51,52,54,56,58,59,60,62,64,66,67,68,70,72,74,75,76,78,79,80,82,83,84,86,88,90,91,92,94,96,98,99,100
>>
>> %N A121538 Increasing sequence: "if n appears then
>> a*n+b doesn't", case a(1)=1, a=2, b=1.
>
> Alternative description:
> Positive integer n is in A121538 iff any of the following is true:
> 1) n is even
> 2) n+1 = 2^k where k is odd
> 3) n+1 = 2^k*(2*t+1) where t>0 and k is even
>
> Max
>
>
> -- 
> No virus found in this incoming message.
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>
>