A334067 -id:A334067 - cp's OEIS frontend

A379051 Lexicographically earliest infinite sequence of distinct positive numbers with the property that n is a member of the sequence iff a(n) is composite.

2, 4, 5, 6, 8, 9, 10, 12, 14, 15, 7, 16, 17, 18, 20, 21, 22, 24, 23, 25, 26, 27, 28, 30, 32, 33, 34, 35, 31, 36, 38, 39, 40, 42, 44, 45, 41, 46, 48, 49, 50, 51, 47, 52, 54, 55, 56, 57, 58, 60, 62, 63, 59, 64, 65, 66, 68, 69, 70, 72, 67, 74, 75, 76, 77, 78, 80

Offset: 1

N. J. A. Sloane, Dec 17 2024

nonn

The sequence tells you exactly which terms of the sequence are composite: the second, fourth, fifth, sixth, etc. terms are composite, and this is the lexicographically earliest sequence with this property.
Let P be a property of the nonnegative integers, such as being a prime.
The OEIS contains many entries whose definitions have the following form.
"The sequence is the lexicographically earliest infinite sequence of distinct positive (or sometimes nonnegative) integers with the property that n is a term of the sequence iff a(n) has property P."
That is, the terms of the sequence tell you which terms of the sequence have the property. A121053 is the classical example.
Since these are lists, the offset is usually 1.
There are two versions, one where the sequence is required to be strictly increasing, and an unrestricted version which is not required to be increasing.
Examples:
  Property P    Unrestricted    Increasing
  ----------------------------------------
  Prime         A121053         A079254, A334067 (offset 0)
  Even          A080032         A079253
  Odd           A079313         A079000
  Composite     A379051         A099797
  Not composite A377901         A099798
  Not prime     A379053         A085925

Michael De Vlieger, Table of n, a(n) for n = 1..65536 [Terms 1 to 10000 from Scott R. Shannon]

Cf. A079000, A079253, A079254, A079313, A080032, A085925, A099797, A099798, A121053, A334067, A377901, A379053.

A379053 Lexicographically earliest infinite sequence of distinct positive numbers with the property that n is a member of the sequence iff a(n) is not a prime.

Original entry on oeis.org

1, 3, 4, 6, 7, 8, 9, 10, 12, 14, 13, 15, 16, 18, 20, 21, 19, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 23, 36, 37, 38, 39, 40, 42, 44, 45, 46, 48, 49, 43, 50, 51, 52, 54, 55, 53, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 61, 70, 72, 74, 75, 76, 77, 78, 71

Offset: 1

N. J. A. Sloane, Dec 17 2024

nonn

The sequence tells you exactly which terms of the sequence are either 1 or composite.

See the Comments in A379051 for further information.

Michael De Vlieger, Table of n, a(n) for n = 1..65536 [Terms 1 to 10000 from Scott R. Shannon]

Cf. A079000, A079253, A079254, A079313, A080032, A085925, A099797, A099798, A121053, A334067, A377901, A379051.

nn = 120; u = 3; v = {}; w = {}; c = 4;
{1}~Join~Reap[Do[
  If[MemberQ[w, n],
    k = c; w = DeleteCases[w, n],
    m = Min[{c, u, v}]; If[And[CompositeQ[m], n < m],
      AppendTo[v, n]];
      If[Length[v] > 0,
        If[v[[1]] == m,
        v = Rest[v]]]; k = m];
    AppendTo[w, k]; If[k == c, c++; While[PrimeQ[c], c++]]; Sow[k];
If[n + 1 >= u, u++; While[CompositeQ[u], u++]], {n, 2, nn}] ][[-1, 1]] (* Michael De Vlieger, Dec 17 2024 *)

When sorted, this appears to be the complement of [2, 5, 11, 17, 29, and prime(2*t+1), t >= 35]. - Scott R. Shannon, Dec 18 2024

More terms from Michael De Vlieger, Dec 17 2024

cp's OEIS Frontend

A379051 Lexicographically earliest infinite sequence of distinct positive numbers with the property that n is a member of the sequence iff a(n) is composite.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions