

A350033


a(n) is the smallest positive integer k not occurring earlier such that Möbius(k) == n mod 3.


0



1, 2, 4, 6, 3, 8, 10, 5, 9, 14, 7, 12, 15, 11, 16, 21, 13, 18, 22, 17, 20, 26, 19, 24, 33, 23, 25, 34, 29, 27, 35, 30, 28, 38, 31, 32, 39, 37, 36, 46, 41, 40, 51, 42, 44, 55, 43, 45, 57, 47, 48, 58, 53, 49, 62, 59, 50, 65, 61, 52, 69, 66, 54, 74, 67, 56, 77, 70
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OFFSET

1,2


COMMENTS

Permutation of the positive integers.
In other words, a(n) is the least positive unusedinteger such that Möbius(a(n)) is respectively 1, 1, 0, 1, 1, 0, 1, 1, 0, ... for n > 0.


LINKS

Table of n, a(n) for n=1..68.


EXAMPLE

a(1) = 1 because 1 is the smallest positive integer with Möbius(1) = 1.
For a(2) we search for the smallest positive integer k not already in the sequence with Möbius(k) = 1. So, a(2) = 2.
Next, we search for Möbius(k) = 0 and a(3) = 6. We continue by asking for the smallest k such that Möbius(k) = 1, 1, 0, 1, 1, 0, ... and so on.


MATHEMATICA

a[1]=1; a[n_]:=a[n]=(k=1; While[MemberQ[Array[a, n1], k]Mod[n, 3, 1]!=MoebiusMu@k, k++]; k); Array[a, 100]


CROSSREFS

Cf. A008683.
Sequence in context: A232846 A101543 A073900 * A351625 A352976 A026200
Adjacent sequences: A350030 A350031 A350032 * A350034 A350035 A350036


KEYWORD

nonn


AUTHOR

Giorgos Kalogeropoulos, Dec 09 2021


STATUS

approved



