

A261690


a(1) = 1; for n>1, a(n) is the smallest number not already present which is entailed by the rules (i) k present => 3*k+1 present; (ii) 2*k present => k present.


6



1, 4, 2, 7, 13, 22, 11, 34, 17, 40, 20, 10, 5, 16, 8, 25, 31, 49, 52, 26, 61, 67, 76, 38, 19, 58, 29, 79, 88, 44, 94, 47, 103, 115, 121, 133, 142, 71, 148, 74, 37, 112, 56, 28, 14, 43, 85, 130, 65, 157, 169, 175, 184, 92, 46, 23, 70, 35, 106, 53, 139, 160, 80
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OFFSET

1,2


COMMENTS

An analog of A109732 such that the statement 'the sequence is a permutation of the positive integers not divisible by 3' is equivalent to the (3*n+1)conjecture for numbers not divisible by 3.
On Aug 29 2015, Max Alekseyev noted that, while the (3*n+1)conjecture indeed implies that the sequence is a permutation of the positive integers not divisible by 3, the opposite statement is an open question. The author cannot yet prove this, so his previous comment is only a conjecture.
In connection with this, consider the following conjecture which could be called the (n1)/3conjecture. Let n be any number not divisible by 3. If n==1 (mod 3) and (n1)/3 is not divisible by 3, then set n_1 = (n1)/3. Otherwise set n_1 = 2*n. Conjecture. There exists an iteration n_m = 1. Does the (n1)/3conjecture imply the (3*n+1)conjecture?
Example: 19>38>76>25>8>16>5>10>20>40>13>4>1.


LINKS

Peter J. C. Moses, Table of n, a(n) for n = 1..10000


CROSSREFS

Cf. A006577, A006877, A006884, A109732.
Sequence in context: A227352 A255140 A108167 * A211941 A050105 A348873
Adjacent sequences: A261687 A261688 A261689 * A261691 A261692 A261693


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Aug 28 2015


STATUS

approved



