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%I #26 Jul 27 2019 12:28:13
%S 3,4,3,2,2,3,2,3,4,5,2,3,2,3,4,5,6,7,8,9,10,11,2,3,2,3,4,5,6,7,8,9,10,
%T 11,12,13,14,15,16,17,18,19,20,21,22,23,2,3,2,3,4,5,6,7,8,9,10,11,12,
%U 13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,2,3,2,3,4,5,2,3,2,3,4,5,6,7,8
%N a(n) = 1 + a(n-1)/gcd(a(n-1),n) with a(0)=3.
%C The behavior of this sequence depends on a(0).
%C For a(0) in {1,4,7,9,19,27,34,47,52,59,63,66,69,71,105,133,147,178,183,202,...} we have a(n) = n.
%C For a(0) in {2,5,10,21,26,35,50,51,53,82,91,96,101,111,122,154,165,170,193,...} we have a(n) = n+2.
%C For other a(0) the sequence is "saw"-like with small irregular periods between saw teeths. For such a(0), a(n) < n/2.
%H Indranil Ghosh, <a href="/A258451/b258451.txt">Table of n, a(n) for n = 0..50000</a>
%e a(0)=3. a(1)=1+3/gcd(3,1)=4. a(2)=1+4/gcd(4,2)=3. a(3)=1+3/gcd(3,3)=2. etc
%t FoldList[1+#1/GCD[#1,#2+1]&,3,Range[0,107]] (* _Ivan N. Ianakiev_, Jun 05 2015 *)
%t nxt[{n_,a_}]:={n+1,1+a/GCD[a,n+1]}; NestList[nxt,{0,3},110][[All,2]] (* _Harvey P. Dale_, Jul 27 2019 *)
%Y Cf. A106108, A084662.
%K nonn
%O 0,1
%A _Ctibor O. Zizka_, May 30 2015
%E Typo in data corrected by _Ivan N. Ianakiev_, Jun 05 2015
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