A258451 a(n) = 1 + a(n-1)/gcd(a(n-1),n) with a(0)=3.

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, 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, 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

Offset: 0

Author

Ctibor O. Zizka, May 30 2015

Keywords

• nonn

Comments

The behavior of this sequence depends on a(0).

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.

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.

For other a(0) the sequence is "saw"-like with small irregular periods between saw teeths. For such a(0), a(n) < n/2.

Examples

			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
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..50000

Crossrefs

Cf. A106108, A084662.

Programs

Mathematica

FoldList[1+#1/GCD[#1,#2+1]&,3,Range[0,107]] (* Ivan N. Ianakiev, Jun 05 2015 *)
nxt[{n_,a_}]:={n+1,1+a/GCD[a,n+1]}; NestList[nxt,{0,3},110][[All,2]] (* Harvey P. Dale, Jul 27 2019 *)

Extensions

Typo in data corrected by Ivan N. Ianakiev, Jun 05 2015