

A163642


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


3



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
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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(k1). 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: A179396 A093491 A140808 * A220533 A085084 A248390
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



