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Search: id:A076536
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| A076536 |
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Image of n at the third step in the 3x+1 Problem: syr(3,n). |
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+0
2
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| 1, 2, 16, 4, 4, 5, 34, 1, 7, 8, 52, 10, 10, 11, 70, 2, 13, 14, 88, 16, 16, 17, 106, 3, 19, 20, 124, 22, 22, 23, 142, 4, 25, 26, 160, 28, 28, 29, 178, 5, 31, 32, 196, 34, 34, 35, 214, 6, 37, 38, 232, 40, 40, 41, 250, 7, 43, 44, 268, 46, 46, 47, 286, 8, 49, 50, 304, 52, 52, 53
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also known as the Collatz Problem, Sysacuse Algorithm or Hailstone Problem. Let syr(m,n) be the image of n at the m-th step. for m=3,k>=0 we get: syr(3,8k)=k, syr(3,8k+1)=6k+1, syr(3,8k+2)=6k+2, syr(3,8k+3)=36k+16, syr(3,8k+4)=6k+4, syr(3,8k+5)=6k+4, syr(3,8k+6)=6k+5, syr(3,8k+7)=36k+34
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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
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FORMULA
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G.f.: (x + 2x^2 + 16x^3 + 4x^4 + 4x^5 + 5x^6 + 34x^7 + x^8 + 5x^9 + 4x^10 + 20x^11 + 2x^12 + 2x^13 + x^14 + 2x^15)/(1-x^8)^2
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EXAMPLE
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1->4->2->1; 2->1->4->2; 3->10->5->16; ...
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CROSSREFS
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Cf. A006370 (n at step 1), A075884 (n at step 2).
Sequence in context: A095860 A070654 A036164 this_sequence A110009 A025586 A087251
Adjacent sequences: A076533 A076534 A076535 this_sequence A076537 A076538 A076539
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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 18 2002
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