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 A118666 Binary polynomials p(x) that are fixed points of the map p(x) -> p(x+1), evaluated as polynomials over Z at x=2. 6
 0, 1, 6, 7, 18, 19, 20, 21, 106, 107, 108, 109, 120, 121, 126, 127, 258, 259, 260, 261, 272, 273, 278, 279, 360, 361, 366, 367, 378, 379, 380, 381, 1546, 1547, 1548, 1549, 1560, 1561, 1566, 1567, 1632, 1633, 1638, 1639, 1650, 1651, 1652, 1653, 1800, 1801 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS If p(x) is a fixed point then P(x):=(x+x^2)*p(x) and P(x)+1 are also fixed points. LINKS Joerg Arndt, Matters Computational (The Fxtbook), section 1.19.3 "Fixed points of the blue code", p.52-54 EXAMPLE a(4)=8 corresponds to the polynomial p(x)=x^4+x (18 is 10010 in binary). p(x+1) = (x+1)^4 + (x+1) = x^4 + 4*x^3 + 6*x^2 + 5*x + 2 = x^4+x = p(x) PROG /* C++ function that returns a unique fixed point for each argument: */ ulong A(ulong s) {   if ( 0==s ) return 0;   ulong f = 1;   while ( s>1 ) { f ^= (f<<1); f <<= 1; f |= (s&1); s >>= 1; }   return f; } /* the elements are not produced in increasing order, but as follows:   0 1 6 7 20 18 21 19 120 108 126 106 121 109 127 107 272 360 ... */ CROSSREFS Cf. A193231 (the map p(x) -> p(x+1)). Sequence in context: A219853 A250196 A260563 * A315847 A030746 A315848 Adjacent sequences:  A118663 A118664 A118665 * A118667 A118668 A118669 KEYWORD nonn AUTHOR Joerg Arndt, May 19 2006, May 20 2006 STATUS approved

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Last modified November 27 21:32 EST 2020. Contains 338684 sequences. (Running on oeis4.)