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A062052
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Numbers with 2 odd integers in their Collatz (or 3x+1) trajectory.
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15
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5, 10, 20, 21, 40, 42, 80, 84, 85, 160, 168, 170, 320, 336, 340, 341, 640, 672, 680, 682, 1280, 1344, 1360, 1364, 1365, 2560, 2688, 2720, 2728, 2730, 5120, 5376, 5440, 5456, 5460, 5461, 10240, 10752, 10880, 10912, 10920, 10922, 20480, 21504, 21760, 21824
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OFFSET
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1,1
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COMMENTS
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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.
The sequence consists of terms of A002450 and their 2^k multiples. The first odd integer in the trajectory is one of the terms of A002450 and the second odd one is the terminal 1. - Antti Karttunen, Feb 21 2006
This sequence looks to appear first in the literature on page 1285 in R. E. Crandall.
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LINKS
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FORMULA
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EXAMPLE
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The Collatz trajectory of 5 is (5,16,8,4,2,1), which contains 2 odd integers.
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MATHEMATICA
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Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; countOdd[lst_] := Length[Select[lst, OddQ]]; Select[Range[22000], countOdd[Collatz[#]] == 2 &] (* T. D. Noe, Dec 03 2012 *)
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PROG
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(PARI) for(n=2, 100000, s=n; t=0; while(s!=1, if(s%2==0, s=s/2, s=3*s+1; t++); if(s*t==1, print1(n, ", "); ); ))
(Haskell)
import Data.List (elemIndices)
a062052 n = a062052_list !! (n-1)
a062052_list = map (+ 1) $ elemIndices 2 a078719_list
(Python)
def a(n):
l=[n, ]
while True:
if n%2==0: n//=2
else: n = 3*n + 1
if n not in l:
l.append(n)
if n<2: break
else: break
return len([i for i in l if i % 2])
print([n for n in range(1, 22001) if a(n)==2]) # Indranil Ghosh, Apr 14 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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