

A213012


Trajectory of 26 under the Reverse and Add! operation carried out in base 2.


1



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

0,1


COMMENTS

26 is the secondsmallest number (after 22) whose base 2 trajectory does not contain a palindrome.
lim_{n > infinity} a(n)/a(n1) = 2 for n mod 2 = 0.
lim_{n > infinity} a(n)/a(n1) = 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


LINKS



EXAMPLE

In binary, 26 is 11010.
a(1) = 37 because 11010 + 01011 = 100101, or 37.
a(2) = 78 because 100101 + 101001 = 1001110, or 78.


MATHEMATICA

binRA[n_] := If[Reverse[IntegerDigits[n, 2]] == IntegerDigits[n, 2], n, FromDigits[Reverse[IntegerDigits[n, 2]], 2] + n]; NestList[binRA, 26, 100]


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



