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A058042
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Trajectory of binary number 10110 under the operation 'Reverse and Add!' carried out in base 2.
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21
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10110, 100011, 1010100, 1101001, 10110100, 11100001, 101101000, 110010101, 1011101000, 1101000101, 10111010000, 11000101101, 101111010000, 110010001101, 1011110100000, 1100001011101, 10111110100000
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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According to J. Walker, Ronald Sprague has proved that this trajectory does not contain a palindrome. [I would like a reference for this.] Another proof has been given by Klaus Brockhaus.
10110 is the smallest number with this property in base 2. The analogous number in base 10 is believed to be 196, but its trajectory (see A006960) has never been proved not to contain a palindrome.
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REFERENCES
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T. Irvin, About Two Months of Computing, or An Addendum to Mr. Walker's Three Years of Computing.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..500
Klaus Brockhaus, On the 'Reverse and Add!' algorithm in base 2
J. Walker, Three Years Of Computing: Final Report On The Palindrome Quest
Index entries for sequences related to Reverse and Add!
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FORMULA
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a(n) = A007088(A061561(n)). - Reinhard Zumkeller, Apr 21 2013
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MATHEMATICA
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Clear[a]; a[0] = 10110; a[n_] := a[n] = (m = IntegerDigits[ a[n-1] ]; m2 = FromDigits[m, 2]; IntegerDigits[ FromDigits[m // Reverse, 2] + m2, 2] // FromDigits); Table[a[n], {n, 0, 16}] (* Jean-François Alcover, Apr 03 2013 *)
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PROG
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(ARIBAS) var m, c, rev: integer; end; m := 22; c := 1; bit_write(m); write(" "); rev := bit_reverse(m); while m <> rev and c < 25 do inc(c); m := m + rev; bit_write(m); write(" "); rev := bit_reverse(m); end;
(Haskell)
a058042 = a007088 . a061561 -- Reinhard Zumkeller, Apr 21 2013
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CROSSREFS
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See A061561 for the terms of A058042 written in base 10. Cf. A016016, A006960, A023108.
Sequence in context: A210892 A114385 A144863 * A191244 A161786 A157711
Adjacent sequences: A058039 A058040 A058041 * A058043 A058044 A058045
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KEYWORD
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nonn,nice,base
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AUTHOR
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N. J. A. Sloane, May 18 2001
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EXTENSIONS
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More terms from Klaus Brockhaus, May 27 2001
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STATUS
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approved
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