A309627 - OEIS

%I #41 Jul 24 2021 02:26:16

%S 6,8,11,12,19,25,30,32,45,46,47,52,53,55,58,59,60,63,64,76,95,97,98,

%T 99,101,102,107,108,114,118,124,126,132,134,137,140,144,152,156,157,

%U 159,163,169,173,177,180,181,185,187,188,189,198,199,200,202,203,206,207,208,209,210

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

%H 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 Brady Haran and N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=pAMgUB51XZA">Amazing Graphs</a>, Numberphile Video.

%e 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 (VBA for Excel)

%o Sub sequence()

%o '

%o For x = 1 To 1002 ' can be made smaller to lessen the processing time

%o    Cells(x, 1) = x - 1 ' generate n for A133058

%o    Cells(1, x) = x - 1 ' generate starting numbers for A133058

%o Next x

%o '

%o For r = 2 To 1002

%o    For c = 2 To 1002

%o       grcd = WorksheetFunction.Gcd(Cells(r - 1, c), Cells(r, 1))

%o       If grcd = 1 Then

%o          Cells(r, c) = Cells(r - 1, c) + Cells(r, 1) + 1

%o       Else

%o          Cells(r, c) = Cells(r - 1, c) / grcd

%o          ' populate an array of the A133058 sequence with a(0)=0,1,2,3,...

%o       End If

%o    Next c

%o Next r

%o '

%o For y = 2 To 1002

%o    If Cells(638, y) = 11 Then

%o       Cells(1005, p + 1) = Cells(1, y)

%o       p = p + 1 ' filter numbers that join the longest sequence

%o    End If

%o Next y

%o '

%o End Sub

%Y Cf. A133058.

%K nonn

%O 1,1

%A _Tomas Tkac_, Aug 10 2019

%E Entry revised by Editors of the OEIS, Oct 01 2019