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

1,1

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

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 *)

Crossrefs

Cf. A085084, A163643.

Sequence in context: A093491 A348512 A140808 * A220533 A357313 A085084

Adjacent sequences: A163639 A163640 A163641 * A163643 A163644 A163645

Keyword

nonn,easy

Author

Leroy Quet, Aug 02 2009

Extensions

More terms from Sean A. Irvine, Nov 11 2009

Status

approved