OFFSET
0,2
COMMENTS
Iteration: multiply by 3 and add 1 and divide out any power of 2; then multiply by 3 and subtract 1 and divide out any power of 2.
When a(x) is iterated, what are the limit cycles? Are there any besides {1} and {17 -> 19 -> 43 -> 97 -> 109 -> 61}?
LINKS
Ray Chandler, Table of n, a(n) for n = 0..10000
EXAMPLE
The iteration for n=13 is 27->61->17->19->43->97->109->61->... and a(13)=1 step was needed to enter the cycle (at 61).
The iteration for n=30 is 61-> 17->19->43->97->109->61->> and the cycle was already entered at the start, so a(30)=0.
MAPLE
A122563 := proc(n)
local cyc, itr, x ;
cyc := [] ;
x := 2*n+1 ;
while true do
cyc := [op(cyc), x] ;
x := A337349(x) ;
if x in cyc then
break ;
end if;
end do:
member(x, cyc, 'itr') ;
itr -1 ;
end proc:
seq(A122563(n), n=0..101) ; # R. J. Mathar, Aug 26 2020
MATHEMATICA
nextx[x_Integer] := Block[{a = x}, a = 3 a + 1; While[EvenQ@a, a /= 2]; a = 3 a - 1; While[EvenQ@a, a /= 2]; a]; f[n_] := Length@NestWhileList[nextx, n, FreeQ[{1, 17, 19, 43, 97, 109, 61}, #] &] - 1; Table[f[2 n + 1], {n, 0, 101}] (* original program from author corrected as suggested by William P. Orrick, Ray Chandler, Aug 28 2020 *)
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Robert G. Wilson v, based on email from Dan Asimov (dasimov(AT)earthlink.net), Sep 20 2006
EXTENSIONS
a(13), a(30),... corrected. - R. J. Mathar, Aug 26 2020
STATUS
approved