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

%I A309627 #41 Jul 24 2021 02:26:16
%S A309627 6,8,11,12,19,25,30,32,45,46,47,52,53,55,58,59,60,63,64,76,95,97,98,
%T A309627 99,101,102,107,108,114,118,124,126,132,134,137,140,144,152,156,157,
%U A309627 159,163,169,173,177,180,181,185,187,188,189,198,199,200,202,203,206,207,208,209,210
%N A309627 Starting numbers k such that the trajectory of k under the map x -> A133058(x) joins A133058.
%H A309627 Tomas Tkac, <a href="/A309627/b309627.txt">Table of n, a(n) for n = 1..306</a> [recomputed and restored by _Georg Fischer_, Oct 14 2019]
%H A309627 Brady Haran and N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=pAMgUB51XZA">Amazing Graphs</a>, Numberphile Video.
%e A309627 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.
%o A309627 (VBA for Excel)
%o A309627 Sub sequence()
%o A309627 '
%o A309627 For x = 1 To 1002 ' can be made smaller to lessen the processing time
%o A309627    Cells(x, 1) = x - 1 ' generate n for A133058
%o A309627    Cells(1, x) = x - 1 ' generate starting numbers for A133058
%o A309627 Next x
%o A309627 '
%o A309627 For r = 2 To 1002
%o A309627    For c = 2 To 1002
%o A309627       grcd = WorksheetFunction.Gcd(Cells(r - 1, c), Cells(r, 1))
%o A309627       If grcd = 1 Then
%o A309627          Cells(r, c) = Cells(r - 1, c) + Cells(r, 1) + 1
%o A309627       Else
%o A309627          Cells(r, c) = Cells(r - 1, c) / grcd
%o A309627          ' populate an array of the A133058 sequence with a(0)=0,1,2,3,...
%o A309627       End If
%o A309627    Next c
%o A309627 Next r
%o A309627 '
%o A309627 For y = 2 To 1002
%o A309627    If Cells(638, y) = 11 Then
%o A309627       Cells(1005, p + 1) = Cells(1, y)
%o A309627       p = p + 1 ' filter numbers that join the longest sequence
%o A309627    End If
%o A309627 Next y
%o A309627 '
%o A309627 End Sub
%Y A309627 Cf. A133058.
%K A309627 nonn
%O A309627 1,1
%A A309627 _Tomas Tkac_, Aug 10 2019
%E A309627 Entry revised by Editors of the OEIS, Oct 01 2019