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A213012
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Trajectory of 26 under the Reverse and Add! operation carried out in base 2.
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1
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26, 37, 78, 135, 360, 405, 744, 837, 1488, 1581, 3024, 3213, 6048, 6237, 12192, 12573, 24384, 24765, 48960, 49725, 97920, 98685, 196224, 197757, 392448, 393981, 785664, 788733, 1571328, 1574397, 3144192, 3150333
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OFFSET
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0,1
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COMMENTS
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26 is the second-smallest number (after 22) whose base 2 trajectory does not contain a palindrome.
lim_{n -> infinity} a(n)/a(n-1) = 2 for n mod 2 = 0.
lim_{n -> infinity} a(n)/a(n-1) = 1 for n mod 2 = 1. - Branman
In 2001, Brockhaus proved that if the binary Reverse and Add trajectory of an integer contains an integer of one of four specific given forms, then the trajectory never reaches a palindrome. In the case of 26, that would be 3(2^(2k + 1) - 2^k), with k = 3 corresponding to 360. - Alonso del Arte, Jun 02 2012
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LINKS
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EXAMPLE
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In binary, 26 is 11010.
a(1) = 37 because 11010 + 01011 = 100101, or 37.
a(2) = 78 because 100101 + 101001 = 1001110, or 78.
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MATHEMATICA
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binRA[n_] := If[Reverse[IntegerDigits[n, 2]] == IntegerDigits[n, 2], n, FromDigits[Reverse[IntegerDigits[n, 2]], 2] + n]; NestList[binRA, 26, 100]
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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