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A288493
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First differences of A006878 (record new trajectory lengths of Collatz function) (Hailstone sequence).
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2
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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
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OFFSET
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1,2
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COMMENTS
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The sequence appears to return to 1 again and again forever when the minimal possible new record of just (previous record + 1) is reached at the latest possible value of 2X. Through 129 there are only 2 entries, a(17) and a(21), that are a minimal new record but aren't 2X.
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LINKS
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EXAMPLE
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For n = 3 the difference between A006878(4) = 8 and A006878(3) = 7 is 1.
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MATHEMATICA
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(* 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}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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