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A079471 Fixed points of reversed binary words in reversed lexicographic order. 1
0, 1, 6, 10, 18, 34, 60, 66, 92, 108, 116, 130, 156, 172, 180, 204, 212, 228, 258, 284, 300, 308, 332, 340, 356, 396, 404, 420, 452, 514, 540, 556, 564, 588, 596, 612, 652, 660, 676, 708, 780, 788, 804, 836, 900, 1026, 1052, 1068, 1076, 1100, 1108, 1124 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

These are 0 and the words where the bit count is 2^i where i is the index of the lowest set bit.

LINKS

Table of n, a(n) for n=0..51.

Joerg Arndt, Fxtbook, section 1.26.4 "The sequence of fixed points", p.73-74

EXAMPLE

Zero is a fixed point: 0: ...........

The next few in decimal and binary form (dots for zeros), lowest (rightmost) bit has index zero are:

1: ............1

6: ..........11.

10: ........1.1.

18: .......1..1.

34: ......1...1.

60: ......1111..

66: .....1....1.

92: .....1.111..

108: ....11.11..

116: ....111.1..

130: ...1.....1.

PROG

(C++):

/* Generate the binary words lex order:

  start with zero and get successive elements via */

inline ulong prev_lexrev(ulong x)

/* Return previous word in (reversed) lex order. */

{

  ulong x0 = x & -x;

  if ( x & (x0<<1) ) x ^= x0;

  else { x0 ^= (x0<<1); x ^= x0; x |= 1; }

  return x;

}

/* To extract the fixed points, select those where

   the following function returns a nonzero value: */

ulong is_lexrev_fixed_point(ulong x)

/* Return whether x is a fixed point in the prev_lexrev() - sequence */

{

  if ( x & 1 ) { if ( 1==x ) return 1; else return 0; }

  else

  {

    ulong w = bit_count(x);

    if ( w != (w & -w) ) return 0;

    if ( 0==x ) return 1; return ( (x & -x) & w );

  }

}

CROSSREFS

Sequence in context: A032641 A293555 A169873 * A134351 A307458 A287273

Adjacent sequences:  A079468 A079469 A079470 * A079472 A079473 A079474

KEYWORD

easy,nonn

AUTHOR

Joerg Arndt, Jan 15 2003

STATUS

approved

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Last modified February 22 14:33 EST 2020. Contains 332136 sequences. (Running on oeis4.)