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Search: id:A001281
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| A001281 |
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Image of n under the map n->n/2 if n even, n->3n-1 if n odd. |
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+0
12
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| 0, 2, 1, 8, 2, 14, 3, 20, 4, 26, 5, 32, 6, 38, 7, 44, 8, 50, 9, 56, 10, 62, 11, 68, 12, 74, 13, 80, 14, 86, 15, 92, 16, 98, 17, 104, 18, 110, 19, 116, 20, 122, 21, 128, 22, 134, 23, 140, 24, 146, 25, 152, 26, 158, 27, 164, 28, 170, 29, 176, 30, 182, 31, 188, 32, 194, 33
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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On the set of positive integers, the orbit of any number seems to end in the orbit of 1, of 5 or of 17. Writing n=1+q*2^p with q odd, it is easily seen that for p=0,1 and p>3, some iterations of the map lead to a strictly smaller number (for n>17). The cases p=2 and p=3 may give rise to bigger loops (depending on the form of q). See sequences A135727-A135729 for maxima of the orbits and corresponding record indices. - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 29 2007
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, E16.
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LINKS
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J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 3-23.
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FORMULA
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f(n) = (7n-2-(5n-2)*cos(pi n))/4 [ Robert W. Craigen (craigen(AT)fresno.edu) ]
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MAPLE
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f := n-> if n mod 2 = 0 then n/2 else 3*n-1; fi;
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PROGRAM
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(PARI) A001281(n)=if(n%2, 3*n-1, n>>1) - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 29 2007
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CROSSREFS
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Cf. A037082.
Cf. A037084, A039500-A039505, A135727-A135730. See also A006370, A006577 (Collatz 3x+1 problem).
Sequence in context: A046740 A130562 A011208 this_sequence A065826 A123235 A140273
Adjacent sequences: A001278 A001279 A001280 this_sequence A001282 A001283 A001284
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KEYWORD
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nonn
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AUTHOR
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njas
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