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Search: id:A075884
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| A075884 |
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Image of n at the second step of the 3x+1 algorithm. |
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+0
2
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| 2, 4, 5, 1, 8, 10, 11, 2, 14, 16, 17, 3, 20, 22, 23, 4, 26, 28, 29, 5, 32, 34, 35, 6, 38, 40, 41, 7, 44, 46, 47, 8, 50, 52, 53, 9, 56, 58, 59, 10, 62, 64, 65, 11, 68, 70, 71, 12, 74, 76, 77, 13, 80, 82, 83, 14, 86, 88, 89, 15, 92, 94, 95, 16, 98, 100, 101, 17, 104, 106, 107
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also known as the Collatz Problem, Syracuse Algorithm or Hailstone Problem. Let syr(m,n) be the image of n at the m-th step. for m=2, k>=0 we get: syr(2,4k)=k, syr(2,4k+1)=6k+2, syr(2,4k+2)=6k+4, syr(2,4k+3)=6k+5
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REFERENCES
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David Wells, Penguin Dictionary of Curious and Interesting Numbers
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LINKS
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Eric Weisstein's World of Mathematics, The Syracuse Algorithm
Eric Weisstein's World of Mathematics, The Syracuse Algorithm at Mathworld
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FORMULA
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G.f.: (x^7+2x^6+4x^5+x^4+5x^3+4x^2+2x)/((1-x^4)^2)
a(n)=(6n+(55n+4)*m-6(5n-2)*m^2+(5n-4)*m^3)/24, m=(n mod 4) (Zak Seidov, Sep 14 2006)
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EXAMPLE
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1->4->2, 2->1->4, 3->10->5, 4->2->1, ...
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CROSSREFS
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Cf. A006370 (the sequence at step 1), A076536 (at step 3).
Sequence in context: A021412 A036501 A167380 this_sequence A030750 A059215 A125142
Adjacent sequences: A075881 A075882 A075883 this_sequence A075885 A075886 A075887
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KEYWORD
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easy,nonn
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AUTHOR
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Bruce Corrigan (scentman(AT)myfamily.com), Oct 16 2002
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