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A181762
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a(n) = n/2 if n is even, otherwise 3n+5.
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4
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0, 8, 1, 14, 2, 20, 3, 26, 4, 32, 5, 38, 6, 44, 7, 50, 8, 56, 9, 62, 10, 68, 11, 74, 12, 80, 13, 86, 14, 92, 15, 98, 16, 104, 17, 110, 18, 116, 19, 122, 20, 128, 21, 134, 22, 140, 23, 146, 24, 152, 25, 158, 26, 164, 27, 170, 28, 176, 29, 182, 30, 188, 31, 194, 32, 200, 33, 206, 34, 212, 35, 218, 36, 224, 37
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OFFSET
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0,2
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COMMENTS
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Has at least two periodic orbits, {1,8,4,2} and {5,20,10}.
Four others are {19,62,31,98,49,152,76,38}, {23,74,37,116,58,29,92,46}, {187,...} and {347,...}. The last two are each of length 44, peaking with 8324 and 10196 respectively. - Geoffrey H. Morley, Mar 14 2013
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REFERENCES
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J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, Amer. Math. Soc., 2010. See p. 307.
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LINKS
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FORMULA
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G.f.: -x*(-8 - x + 2*x^2) / ( (x-1)^2*(1+x)^2 ). - R. J. Mathar, Mar 10 2011
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MAPLE
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f:=n->if n mod 2 = 0 then n/2 else 3*x+5 fi;
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MATHEMATICA
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Table[If[EvenQ[n], n/2, 3n+5], {n, 0, 80}] (* Harvey P. Dale, Nov 25 2023 *)
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PROG
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(Magma) [(7*n+10-10*(-1)^n*(n/2+1))/4: n in [0..80]]; // Vincenzo Librandi, May 24 2011
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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