

A294643


Length (= size) of the orbit of n under the "3x+1" map A006370: x > x/2 if even, 3x+1 if odd. a(n) = 1 in case the orbit would be infinite.


0



1, 3, 3, 8, 3, 6, 9, 17, 4, 20, 7, 15, 10, 10, 18, 18, 5, 13, 21, 21, 8, 8, 16, 16, 11, 24, 11, 112, 19, 19, 19, 107, 6, 27, 14, 14, 22, 22, 22, 35, 9, 110, 9, 30, 17, 17, 17, 105, 12, 25, 25, 25, 12, 12, 113, 113, 20, 33, 20, 33, 20, 20, 108, 108, 7, 28, 28
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OFFSET

0,2


COMMENTS

The orbit of x under f is O(x; f) = { f^k(x); k = 0, 1, 2, ... }, i.e., the set of all points in the trajectory of x under iterations of f.
The famous "3x+1 problem" or Collatz conjecture (also attributed to other names) states that for f = A006370, the trajectory (f^k(x); k >= 0) always ends in the cycle 1 > 4 > 2 > 1, for any integer starting value x >= 0.


LINKS

Table of n, a(n) for n=0..66.


EXAMPLE

a(0) = 1 = # { 0 }, since 0 > 0 > 0 ... under A006370.
a(1) = 3 = # { 1, 4, 2 }, since 1 > (3*1 + 1 =) 4 > 2 > 1 > 4 etc. under A006370.
a(3) = 8 = # { 3, 10, 5, 16, 8, 4, 2, 1 }, since 3 > 10 > 5 > 16 > 8 > 4 > 2 > 1 > 4 etc. under A006370.


CROSSREFS

Cf. A006370 (Collatz or 3x+1 map), A008908 (number of steps to reach 1), A174221 (the "PrimeLatz" map: add 3 next primes), A293980, A293975 (variant: add the next prime), A293982.
Sequence in context: A154178 A276800 A212809 * A029614 A143615 A199337
Adjacent sequences: A294640 A294641 A294642 * A294644 A294645 A294646


KEYWORD

nonn


AUTHOR

M. F. Hasler, Nov 05 2017


STATUS

approved



