%I #24 Oct 21 2022 22:07:49

%S 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,

%T 80,14,86,15,92,16,98,17,104,18,110,19,116,20,122,21,128,22,134,23,

%U 140,24,146,25,152,26,158,27,164,28,170,29,176,30,182,31,188

%N Image of n under the map n->n/2 if n even, n->3n-1 if n odd.

%C 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

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

%H T. D. Noe, <a href="/A001281/b001281.txt">Table of n, a(n) for n = 0..1000</a>

%H J. C. Lagarias, <a href="http://www.cecm.sfu.ca/organics/papers/lagarias/paper/html/paper.html">The 3x+1 problem and its generalizations</a>, Amer. Math. Monthly, 92 (1985), 3-23.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1)

%F f(n) = (7n-2-(5n-2)*cos(Pi*n))/4. - Robert W. Craigen (craigen(AT)fresno.edu)

%F G.f.: x*(2 + x + 4*x^2)/((1 - x)^2*(1 + x)^2). - _Ilya Gutkovskiy_, Aug 17 2016

%p f := n-> if n mod 2 = 0 then n/2 else 3*n-1; fi;

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

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

%Y Cf. A037082.

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

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_