A163642 a(n) = the smallest composite positive integer that is not yet in the sequence and that is coprime to n.

4, 9, 8, 15, 6, 25, 10, 21, 14, 27, 12, 35, 16, 33, 22, 39, 18, 49, 20, 51, 26, 45, 24, 55, 28, 57, 32, 65, 30, 77, 34, 63, 38, 69, 36, 85, 40, 75, 44, 81, 42, 95, 46, 87, 52, 91, 48, 115, 50, 93, 56, 99, 54, 119, 58, 111, 62, 105, 60, 121, 64, 117, 68, 123, 66, 125, 70, 129, 74

Offset: 1

Author

Leroy Quet, Aug 02 2009

Keywords

• nonn
• easy

Comments

This sequence is a permutation of the composite positive integers.

Indices of composites: {1, 4, 3, 8, 2, 15, 5, 12, 7, 17, 6, 23, 9, 21, 13, 26, 10, 33, 11, 35, 16, 30, 14, 38, 18, 40, 20, 46, ...}. - Michael De Vlieger, Jul 23 2017

Each composite k occurs in the sequence no later than a(k-1). Proof by induction. - Peter Munn, Sep 01 2017

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A085084, A163643.

Programs

Mathematica

a = {4}; Do[k = 6; While[Nand[CompositeQ@ k, ! MemberQ[a, k], CoprimeQ[k, n]], k++]; AppendTo[a, k], {n, 2, 69}]; a (* Michael De Vlieger, Jul 23 2017 *)

Extensions

More terms from Sean A. Irvine, Nov 11 2009