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A079471 Fixed points of reversed binary words in reversed lexicographic order.

%I A079471 #18 Feb 18 2024 01:26:01
%S A079471 0,1,6,10,18,34,60,66,92,108,116,130,156,172,180,204,212,228,258,284,
%T A079471 300,308,332,340,356,396,404,420,452,514,540,556,564,588,596,612,652,
%U A079471 660,676,708,780,788,804,836,900,1026,1052,1068,1076,1100,1108,1124
%N A079471 Fixed points of reversed binary words in reversed lexicographic order.
%C A079471 These are 0 and the words where the bit count is 2^i where i is the index of the lowest set bit.
%H A079471 Paolo Xausa, <a href="/A079471/b079471.txt">Table of n, a(n) for n = 0..10000</a>
%H A079471 Joerg Arndt, <a href="http://www.jjj.de/fxt/fxtpage.html#fxtbook">Fxtbook</a>, section 1.26.4 "The sequence of fixed points", p.73-74
%e A079471 Zero is a fixed point: 0: ...........
%e A079471 The next few in decimal and binary form (dots for zeros), lowest (rightmost) bit has index zero are:
%e A079471 1: ............1
%e A079471 6: ..........11.
%e A079471 10: ........1.1.
%e A079471 18: .......1..1.
%e A079471 34: ......1...1.
%e A079471 60: ......1111..
%e A079471 66: .....1....1.
%e A079471 92: .....1.111..
%e A079471 108: ....11.11..
%e A079471 116: ....111.1..
%e A079471 130: ...1.....1.
%t A079471 Join[{0},Select[Range[10^4],DigitCount[#,2,1]==2^IntegerExponent[#,2]&]] (* _Paolo Xausa_, Nov 13 2023 *)
%o A079471 (C++)
%o A079471 /* Generate the binary words lex order:
%o A079471   start with zero and get successive elements via */
%o A079471 inline ulong prev_lexrev(ulong x)
%o A079471 /* Return previous word in (reversed) lex order. */
%o A079471 {
%o A079471   ulong x0 = x & -x;
%o A079471   if ( x & (x0<<1) ) x ^= x0;
%o A079471   else { x0 ^= (x0<<1); x ^= x0; x |= 1; }
%o A079471   return x;
%o A079471 }
%o A079471 /* To extract the fixed points, select those where
%o A079471    the following function returns a nonzero value: */
%o A079471 ulong is_lexrev_fixed_point(ulong x)
%o A079471 /* Return whether x is a fixed point in the prev_lexrev() - sequence */
%o A079471 {
%o A079471   if ( x & 1 ) { if ( 1==x ) return 1; else return 0; }
%o A079471   else
%o A079471   {
%o A079471     ulong w = bit_count(x);
%o A079471     if ( w != (w & -w) ) return 0;
%o A079471     if ( 0==x ) return 1; return ( (x & -x) & w );
%o A079471   }
%o A079471 }
%K A079471 easy,nonn
%O A079471 0,3
%A A079471 _Joerg Arndt_, Jan 15 2003