A119018 a(1) = 1; a(n) is the smallest number not yet used that is not relatively prime to n nor relatively prime to a(n-1).

1, 2, 6, 4, 10, 8, 14, 12, 3, 15, 33, 9, 39, 18, 20, 16, 34, 22, 38, 24, 21, 28, 46, 26, 30, 32, 36, 40, 58, 42, 62, 44, 11, 66, 45, 27, 111, 48, 51, 54, 82, 50, 86, 52, 60, 56, 94, 64, 70, 5, 75, 65, 265, 80, 25, 35, 63, 72, 118, 68, 122, 74, 78, 76, 90, 55, 335, 85, 102, 84, 142

Offset: 1

Author

Franklin T. Adams-Watters, May 08 2006

Keywords

• nonn

Comments

Conjecture: this sequence includes every integer greater than 1.

In the first 200000 terms the only fixed points are 2, 4, 16, 21, 95, 159, 723, 18071. - Scott R. Shannon, Oct 25 2024

Examples

			a(12) must have a common factor with 12 and a(11) = 33. The first few such values are 3, 6 and 9; 3 and 6 have already been used, so a(12)=9.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000
• Scott R. Shannon, Image of the first 200000 terms for a(n) < 400000. The green line is a(n) = n.

Crossrefs

Cf. A119019.

Programs

Maple

A119018 := proc(nmin) local a,anxt ; a := [0] ; while nops(a) < nmin do anxt := 1 ; n := nops(a)+1 ; while anxt in a or gcd(n,anxt) = 1 or gcd(op(-1,a),anxt) = 1 do anxt := anxt+1 ; od ; a := [op(a),anxt]; od: RETURN(a) ; end: A119018(100) ; # R. J. Mathar, Sep 07 2007

Mathematica

a = {0}; Do[k = 1; While[MemberQ[a, k] || GCD[k, n] == 1 || GCD[k, a[[-1]]] == 1, k++]; AppendTo[a, k], {n, 2, 71}]; a (* Ivan Neretin, Jul 09 2015 *)

Extensions

Definition corrected by R. J. Mathar, Sep 07 2007

a(1) changed to a(1) = 1 by Scott R. Shannon, Oct 28 2024