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A171490
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Numbers for which the smallest number of steps to reach 1 in "3x+1" (or Collatz) problem is a prime.
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1
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1, 5, 7, 12, 14, 16, 29, 51, 56, 58, 60, 64, 65, 67, 74, 75, 78, 83, 87, 90, 100, 102, 104, 106, 109, 115, 118, 119, 122, 128, 130, 132, 134, 141, 142, 147, 161, 166, 173, 176, 187, 188, 200, 212, 219, 221, 231, 234, 239, 241, 251, 259, 264, 293, 313, 314, 316
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OFFSET
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1,2
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COMMENTS
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REFERENCES
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R. K. Guy, "Collatz's Sequence" in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 215-218, 1994
Clifford A. Pickover, Wonders of Numbers, Oxford University Press, pp. 116-118, 2001
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LINKS
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EXAMPLE
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1st Collatz sequence with a(1)=1 step starts with 2=prime(1): 2-1;
1st Collatz sequence with a(3)=7 steps starts with 3=prime(2): 3-10-5-16-8-4-2-1;
prime(6)=13 has Collatz sequence with 9 steps: 13-40-20-10-5-16-8-4-2-1, so has the smaller composite 12 < 13: 12-6-3-10-5-16-8-4-2-1 => 9 not a term of sequence;
1st Collatz sequence with a(5)=14 steps starts with 11=prime(5): 11-34-17-52-26-13-40-20-10-5-16-8-4-2-1.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Ulrich Krug (leuchtfeuer37(AT)gmx.de), Dec 10 2009
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EXTENSIONS
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STATUS
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approved
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