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

zak seidov zakseidov at yahoo.com
Sun Aug 6 10:48:54 CEST 2006

```Dear seqfans,
I'm going to submit A121538.
1. Is it any general formula for a(n)?
2. First differences d(n) are:

1,2,2,1,1,2,1,1,2,2,2,1,1,2,2,2,1,1,2,1,1,2,1,1,2,2,2,1,1,2,1,1,2,1,1,2,2,2,1,1,2,2,2,1,1,2,2,2,1,1,2,1,1,2,1,1,2,2,2,1,1,2,2,2,1,1,2,2,2,1,1,2,1,1,2,1,1,2,2,2,1,1,2,1,1,2,1,1,2,2,2,1,1,2,1,1,2,1,1,2,2,2,1,1,2,2,2,1,1,2,2,2,1,1,2,1,1,2,1,1,2,2,2,1,1,2,1,1,2,1,1,2,2,...

some patterns are vaguely appearing...
Any general formula for d(n)?
Thanks, Zak

Subject: PRE-NUMBERED NEW SEQUENCE A121538 FROM Zak
Seidov
%I A121538
%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.
%t A121538
s={s1=1};With[{a=2,b=1},Do[If[FreeQ[s,(n-b)/a],AppendTo[s,n]],{n,s1+1,100}]];s

%Y A121538 A121539, A121540, A121541, A121542
%O A121538 1
%K A121538 ,nonn,
%A A121538 Zak Seidov (zakseidov at yahoo.com), Aug 06
2006

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