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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.
1
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
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.
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: A276800 A332684 A212809 * A029614 A143615 A199337
KEYWORD
nonn
AUTHOR
M. F. Hasler, Nov 05 2017
STATUS
approved