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A263716
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Irregular triangle read by rows: numbers in the Collatz conjecture in the order of their first appearance.
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4
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1, 2, 3, 10, 5, 16, 8, 4, 6, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 9, 28, 14, 12, 15, 46, 23, 70, 35, 106, 53, 160, 80, 18, 19, 58, 29, 88, 44, 21, 64, 32, 24, 25, 76, 38, 27, 82, 41, 124, 62, 31, 94, 47, 142, 71, 214, 107, 322, 161, 484, 242, 121, 364, 182
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refs;
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OFFSET
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0,2
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COMMENTS
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This is the irregular triangle read by rows giving trajectory of n in the Collatz problem, flattened and with all the repeated terms deleted.
This sequence goes to infinity as n gets larger. On the Collatz conjecture this sequence is a permutation of the positive integers. [Corrected by Charles R Greathouse IV, Jul 29 2016]
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LINKS
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FORMULA
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row(n) = {
if seen[n]: stop
else: write(n) and do:
| n is one: stop
| n is odd: n <- 3*n+1
| n is even: n <- n/2
}
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EXAMPLE
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Triangle begins:
1;
2;
3, 10, 5, 16, 8, 4;
...
The Collatz trajectories for the first five positive integers are {1}, {2, 1}, {3, 10, 5, 16, 8, 4, 2, 1}, {4, 2, 1}, {5, 16, 8, 4, 2, 1}.
From {2, 1} we delete 1 because it has already occurred. From {3, 10, 5, ..., 4, 2, 1} we delete {2, 1} because both numbers have already occurred. We completely get rid of {4, 2, 1} because it has already occurred as the tail end of {3, 10, 5, ...}, and we also completely get rid of {5, 16, 8, ...} for the same reason.
This leaves us with {1}, {2}, {3, 10, 5, 16, 8, 4}, thus accounting for the first eight terms of this sequence.
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MATHEMATICA
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collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; DeleteDuplicates[Flatten[Table[collatz[n], {n, 20}]]] (* Alonso del Arte, Oct 24 2015 *)
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PROG
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(Sidef)
func collatz(n) is cached { # automatically memoized function
say n; # prints the first unseen numbers
n.is_one ? 0
: (n.is_even ? collatz(n/2)
: collatz(3*n + 1));
}
range(1, Math.inf).each { |i| collatz(i) }
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CROSSREFS
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Cf. A347265 (essentially the same).
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KEYWORD
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nonn,tabf,easy,nice
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AUTHOR
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STATUS
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approved
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