

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

T. D. Noe, Table of n, a(n) for n = 0..1000
J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 323.
Index entries for linear recurrences with constant coefficients, signature (0,2,0,1)


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

(PARI) A001281(n)=if(n%2, 3*n1, n>>1) \\ M. F. Hasler, Nov 29 2007


CROSSREFS

Cf. A037082.
Cf. A037084, A039500A039505, A135727A135730. See also A006370, A006577 (Collatz 3x+1 problem).
Sequence in context: A154175 A257777 A011208 * A331312 A232535 A065826
Adjacent sequences: A001278 A001279 A001280 * A001282 A001283 A001284


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


STATUS

approved



