A309627 Starting numbers k such that the trajectory of k under the map x -> A133058(x) joins A133058.

6, 8, 11, 12, 19, 25, 30, 32, 45, 46, 47, 52, 53, 55, 58, 59, 60, 63, 64, 76, 95, 97, 98, 99, 101, 102, 107, 108, 114, 118, 124, 126, 132, 134, 137, 140, 144, 152, 156, 157, 159, 163, 169, 173, 177, 180, 181, 185, 187, 188, 189, 198, 199, 200, 202, 203, 206, 207, 208, 209, 210

Offset

1,1

Links

Tomas Tkac, Table of n, a(n) for n = 1..306 [recomputed and restored by Georg Fischer, Oct 14 2019]

Brady Haran and N. J. A. Sloane, Amazing Graphs, Numberphile Video.

Example

Quite a few starting numbers f(0) for the recurrence defined in A133058 will produce a sequence which eventually join A133058, the smallest such number being 6. 8 joins 6 at the 10th term, 11 joins 6 at the 17th term, 12 joins the sequence at the 97th term, etc.

Prog

(VBA for Excel)
Sub sequence()
'
For x = 1 To 1002 ' can be made smaller to lessen the processing time
   Cells(x, 1) = x - 1 ' generate n for A133058
   Cells(1, x) = x - 1 ' generate starting numbers for A133058
Next x
'
For r = 2 To 1002
   For c = 2 To 1002
      grcd = WorksheetFunction.Gcd(Cells(r - 1, c), Cells(r, 1))
      If grcd = 1 Then
         Cells(r, c) = Cells(r - 1, c) + Cells(r, 1) + 1
      Else
         Cells(r, c) = Cells(r - 1, c) / grcd
         ' populate an array of the A133058 sequence with a(0)=0, 1, 2, 3, ...
      End If
   Next c
Next r
'
For y = 2 To 1002
   If Cells(638, y) = 11 Then
      Cells(1005, p + 1) = Cells(1, y)
      p = p + 1 ' filter numbers that join the longest sequence
   End If
Next y
'
End Sub

Crossrefs

Cf. A133058.

Sequence in context: A235599 A242778 A184113 * A085412 A228650 A358531

Adjacent sequences: A309624 A309625 A309626 * A309628 A309629 A309630

Keyword

nonn

Author

Tomas Tkac, Aug 10 2019

Extensions

Entry revised by Editors of the OEIS, Oct 01 2019

Status

approved