

A001281


Image of n under the map n>n/2 if n even, n>3n1 if n odd.


14



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
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OFFSET

0,2


COMMENTS

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 A135727A135729 for maxima of the orbits and corresponding record indices.  M. F. Hasler, Nov 29 2007


REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, E16.


LINKS



FORMULA

f(n) = (7n2(5n2)*cos(Pi*n))/4.  Robert W. Craigen (craigen(AT)fresno.edu)
G.f.: x*(2 + x + 4*x^2)/((1  x)^2*(1 + x)^2).  Ilya Gutkovskiy, Aug 17 2016


MAPLE

f := n> if n mod 2 = 0 then n/2 else 3*n1; fi;


MATHEMATICA

Table[If[OddQ[n], 3*n1, n/2], {n, 0, 100}] (* T. D. Noe, Jun 27 2012 *)


PROG



CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



