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A263716 Numbers in the Collatz conjecture in the order of their first appearance. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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]

LINKS

Daniel Suteu, Table of n, a(n) for n = 0..19999

FORMULA

a(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

}

EXAMPLE

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.

MATHEMATICA

collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; DeleteDuplicates[Flatten[Table[collatz[n], {n, 20}]]] (* Alonso del Arte, Oct 24 2015 *)

PROG

(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) }

CROSSREFS

Cf. A070165.

Sequence in context: A139693 A182076 A266552 * A175899 A328613 A064946

Adjacent sequences:  A263713 A263714 A263715 * A263717 A263718 A263719

KEYWORD

nonn,easy,nice

AUTHOR

Daniel Suteu, Oct 24 2015

STATUS

approved

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Last modified November 17 03:06 EST 2019. Contains 329216 sequences. (Running on oeis4.)