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A062053
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Numbers with 3 odd integers in their Collatz (or 3x+1) trajectory.
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5
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3, 6, 12, 13, 24, 26, 48, 52, 53, 96, 104, 106, 113, 192, 208, 212, 213, 226, 227, 384, 416, 424, 426, 452, 453, 454, 768, 832, 848, 852, 853, 904, 906, 908, 909, 1536, 1664, 1696, 1704, 1706, 1808, 1812, 1813, 1816, 1818, 3072, 3328, 3392, 3408, 3412, 3413, 3616
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The Collatz (or 3x+1) function is f(x) = x/2 if x is even, 3x+1 if x is odd.
The Collatz trajectory of n is obtained by applying f repeatedly to n until 1 is reached.
Sequence is 2-automatic.
A078719(a(n)) = 3; A006667(a(n)) = 2.
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REFERENCES
| J. R. Goodwin, Results on the Collatz Conjecture, Sci. Ann. Comput. Sci. 13 (2003) pp. 1-16
J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185.
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..250
J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185.
Eric Weisstein's World of Mathematics, CollatzProblem
Wikipedia, Collatz conjecture
Index entries for sequences related to 3x+1 (or Collatz) problem
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FORMULA
| The two formulas giving this sequence are listed in Corollary 3.1 and Corollary 3.2 in J. R. Goodwin with the following caveats: the value x cannot equal zero in Corollary 3.2, one must multiply the formulas by all powers of 2 (2^1, 2^2, ...) to get the evens. - Jeffrey R. Goodwin, Oct 26 2011
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EXAMPLE
| The Collatz trajectory of 3 is (3,10,5,16,8,4,2,1), which contains 3 odd integers.
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MATHEMATICA
| Collatz[n_?OddQ] := (3n + 1)/2; Collatz[n_?EvenQ] := n/2; oddIntCollatzCount[n_] := Length[Select[NestWhileList[Collatz, n, # != 1 &], OddQ]]; Select[Range[4000], oddIntCollatzCount[#] == 3 &] (* Alonso del Arte, Oct 28 2011 *)
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PROG
| (Haskell)
import Data.List (elemIndices)
a062053 n = a062053_list !! (n-1)
a062053_list = map (+ 1) $ elemIndices 3 a078719_list
-- Reinhard Zumkeller, Oct 08 2011
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CROSSREFS
| Cf. A062052-A062060.
Cf. A198584 (this sequence without the even numbers).
Sequence in context: A078502 A107974 A116625 * A102040 A077152 A067759
Adjacent sequences: A062050 A062051 A062052 * A062054 A062055 A062056
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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