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A062055 Numbers with 5 odd integers in their Collatz (or 3x+1) trajectory. 8
11, 22, 23, 44, 45, 46, 88, 90, 92, 93, 176, 180, 181, 184, 186, 201, 352, 360, 362, 368, 369, 372, 373, 401, 402, 403, 704, 720, 724, 725, 736, 738, 739, 744, 746, 753, 802, 803, 804, 805, 806, 1408, 1440, 1448, 1450, 1472, 1476, 1477, 1478, 1488, 1492, 1493, 1506 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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.
A078719(a(n)) = 5; A006667(a(n)) = 4.
REFERENCES
J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185.
LINKS
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, Collatz Problem
EXAMPLE
The Collatz trajectory of 11 is (11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1), which contains 5 odd integers.
MATHEMATICA
Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; countOdd[lst_] := Length[Select[lst, OddQ]]; Select[Range[2000], countOdd[Collatz[#]] == 5 &] (* T. D. Noe, Dec 03 2012 *)
PROG
(Haskell)
import Data.List (elemIndices)
a062055 n = a062055_list !! (n-1)
a062055_list = map (+ 1) $ elemIndices 5 a078719_list
-- Reinhard Zumkeller, Oct 08 2011
CROSSREFS
Column k=5 of A354236.
Sequence in context: A297273 A296746 A095779 * A332516 A066500 A234314
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)