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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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14
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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
(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.
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
A078719(a(n)) = 2; A006667(a(n)) = 1.
This sequence looks to appear first in the literature on page 1285 in R. E. Crandall.
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REFERENCES
| J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185.
R. E. Crandall, On the "3x+1" Problem, Math. Comp. 32(144) (1978) pp. 1281-1292.
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..100
J. Shallit and D. Wilson, The "3x+1" Problem and Finite Automata, Bulletin of the EATCS #46 (1992) pp. 182-185.
Wikipedia, Collatz conjecture
Eric Weisstein's World of Mathematics, CollatzProblem
Index entries for sequences related to 3x+1 (or Collatz) problem
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EXAMPLE
| The Collatz trajectory of 5 is (5,16,8,4,2,1), which contains 2 odd integers.
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PROG
| (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
-- Reinhard Zumkeller, Oct 08 2011
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CROSSREFS
| Cf. A062053-A062060.
Is this a subset of A115774?.
Sequence in context: A147390 A115825 A115774 * A115799 A072703 A086761
Adjacent sequences: A062049 A062050 A062051 * A062053 A062054 A062055
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KEYWORD
| nonn
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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