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 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 (list; graph; refs; listen; history; text; internal format)
 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 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, n-1], 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

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Last modified August 7 20:35 EDT 2022. Contains 355994 sequences. (Running on oeis4.)