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Search: id:A062052
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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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+0
12
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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; listen)
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OFFSET
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1,1
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COMMENT
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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.
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
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REFERENCES
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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
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Index entries for sequences related to 3x+1 (or Collatz) problem
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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PROGRAM
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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, ", "); ); ))
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CROSSREFS
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Cf. A062053-A062060.
Is this a subset of A115774?.
Adjacent sequences: A062049 A062050 A062051 this_sequence A062053 A062054 A062055
Sequence in context: A053311 A115825 A115774 this_sequence A115799 A072703 A086761
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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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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