%I #24 Dec 18 2023 12:21:53
%S 0,1,6,7,18,19,20,21,106,107,108,109,120,121,126,127,258,259,260,261,
%T 272,273,278,279,360,361,366,367,378,379,380,381,1546,1547,1548,1549,
%U 1560,1561,1566,1567,1632,1633,1638,1639,1650,1651,1652,1653,1800,1801
%N Binary polynomials p(x) that are fixed points of the map p(x) -> p(x+1), evaluated as polynomials over Z at x=2.
%C If p(x) is a fixed point then P(x):=(x+x^2)*p(x) and P(x)+1 are also fixed points.
%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, section 1.19.3 "Fixed points of the blue code", p.52-54
%H <a href="/index/Ge#GF2X">Index entries for sequences operating on (or containing) GF(2)[X]-polynomials</a>
%e a(4)=18 corresponds to the polynomial p(x)=x^4+x (18 is 10010 in binary).
%e p(x+1) = (x+1)^4 + (x+1) = x^4 + 4*x^3 + 6*x^2 + 5*x + 2 = x^4+x = p(x);
%o /* C++ function that returns a unique fixed point for each argument: */
%o ulong A(ulong s)
%o {
%o if ( 0==s ) return 0;
%o ulong f = 1;
%o while ( s>1 ) { f ^= (f<<1); f <<= 1; f |= (s&1); s >>= 1; }
%o return f;
%o }
%o /* the elements are not produced in increasing order, but as follows:
%o 0 1 6 7 20 18 21 19 120 108 126 106 121 109 127 107 272 360 ... */
%Y Cf. A193231 (the map p(x) -> p(x+1)).
%K nonn
%O 0,3
%A _Joerg Arndt_, May 19 2006, May 20 2006