login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A001281 Image of n under the map n->n/2 if n even, n->3n-1 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 (list; graph; refs; listen; history; text; internal format)
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 A135727-A135729 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), 3-23.

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1)

FORMULA

f(n) = (7n-2-(5n-2)*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*n-1; fi;

MATHEMATICA

Table[If[OddQ[n], 3*n-1, n/2], {n, 0, 100}] (* T. D. Noe, Jun 27 2012 *)

PROG

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

CROSSREFS

Cf. A037082.

Cf. A037084, A039500-A039505, A135727-A135730. See also A006370, A006577 (Collatz 3x+1 problem).

Sequence in context: A154175 A257777 A011208 * A232535 A065826 A286899

Adjacent sequences:  A001278 A001279 A001280 * A001282 A001283 A001284

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified September 23 17:26 EDT 2017. Contains 292361 sequences.