A288493 First differences of A006878 (record new trajectory lengths of Collatz function) (Hailstone sequence).
1, 6, 1, 8, 3, 1, 3, 88, 1, 3, 3, 3, 3, 3, 3, 13, 1, 26, 8, 3, 1, 26, 8, 21, 24, 6, 8, 3, 3, 26, 3, 13, 16, 11, 3, 21, 8, 3, 57, 6, 21, 39, 16, 3, 3, 26, 3, 3, 21, 13, 16, 52, 21, 3, 3, 13, 1, 39, 205, 1, 3, 3, 8, 1, 21, 1, 13, 8, 42, 37, 44, 1, 21, 31, 26, 3, 6, 1, 8, 6, 8, 13, 52, 1, 13, 3, 8, 3, 13, 8, 52, 3, 26, 3, 3, 106, 1, 13, 3, 3, 16, 3, 13, 16, 21, 13, 8
Offset: 1
Keywords
Examples
For n = 3 the difference between A006878(4) = 8 and A006878(3) = 7 is 1.
Links
- Hugo Pfoertner, Table of n, a(n) for n = 1..147 (from Eric Rosendaal's 3x+1 Delay Records, terms 1..129 from David Rabahy)
- Eric Roosendaal, 3x+1 Delay Records
Programs
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Mathematica
(* This script is not suitable to compute a large number of terms. *) terms = 40; steps[x0_] := steps[x0] = Block[{x = x0, nos = 0}, While[x != 1, If[Mod[x, 2] == 0, x = x/2, x = 3*x + 1]; nos++]; nos]; b[1] = 1; b[n_] := b[n] = Block[{x = b[n - 1] + 1}, record = steps[x - 1]; While[steps[x] <= record, x++]; x]; A006877 = Table[Print[b[n]]; b[n], {n, 1, terms+1}]; A006878 = steps /@ A006877; Differences[A006878] (* Jean-François Alcover, Jun 15 2017 *)
Comments