The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A185000 Trajectory of x+1 under the map (see A185544) defined in the Comments. 3
 11, 111, 1101, 11100, 1110, 111, 1101, 11100, 1110, 111, 1101, 11100, 1110, 111, 1101, 11100, 1110, 111, 1101, 11100, 1110, 111, 1101, 11100, 1110, 111, 1101, 11100, 1110, 111, 1101, 11100, 1110, 111, 1101, 11100, 1110, 111, 1101, 11100, 1110, 111, 1101, 11100, 1110, 111, 1101, 11100, 1110, 111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS We work in the ring GF(2)[x]. The map is f->f/x if f(0)=0, otherwise f->((x^2+1)f+1)/x. We represent polynomials by their vector of coefficients, high powers first. See A185544. REFERENCES J. C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, Amer. Math. Soc., 2010; see page 99. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (0,0,0,1). FORMULA From Colin Barker, Aug 23 2018: (Start) G.f.: x*(11 + 111*x + 1101*x^2 + 11100*x^3 + 1099*x^4) / ((1 - x)*(1 + x)*(1 + x^2)). a(n) = a(n-4) for n>5. (End) EXAMPLE The trajectory is x^2+x+1, x^3+x^2+1, x^4+x^3+x^2, x^3+x^2+x, x^2+x+1, x^3+x^2+1, x^4+x^3+x^2, x^3+x^2+x, x^2+x+1, x^3+x^2+1, ..., with period 4. MAPLE # Extract coefficient vector polynomial (decreasing powers): coeflistD:=proc(f) local d, i, t1, t2, t3, t4; if f=0 then RETURN([0]); else d:=degree(f); t1:=subs(x=1/x, f); t2:=sort(expand(x^d*t1)); t3:=seriestolist(series(t2, x, d+2)); t4:=nops(t3); if t4if subs(x=0, a) = 0 then expand(simplify(a/x)) mod 2; else t1:=((x^2+1)*a+1)/x;  expand(t1) mod 2; fi; # Get trajectory (as both polynomials and coefficient vectors): T:=proc(n, M) global f, coeflistD; local t1, i, s1; t1:=[n]; for i from 1 to M-1 do t1:=[op(t1), f(t1[nops(t1)])]; od: lprint(t1); s1:=[]; for i from 1 to M do s1:=[op(s1), coeflistD(t1[i])]; od: lprint(s1); end; T(x+1, 12); PROG (PARI) Vec(x*(11 + 111*x + 1101*x^2 + 11100*x^3 + 1099*x^4) / ((1 - x)*(1 + x)*(1 + x^2)) + O(x^50)) \\ Colin Barker, Aug 23 2018 CROSSREFS Cf. A185544. Sequence in context: A284024 A283175 A284274 * A283585 A283703 A284399 Adjacent sequences:  A184997 A184998 A184999 * A185001 A185002 A185003 KEYWORD nonn AUTHOR N. J. A. Sloane, Feb 05 2011 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 22 21:47 EST 2022. Contains 350504 sequences. (Running on oeis4.)