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A075252
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Trajectory of n under the Reverse and Add! operation carried out in base 2 does not reach a palindrome and (presumably) does not join the trajectory of any term m < n.
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12
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22, 77, 442, 537, 775, 1066, 1081, 1082, 1085, 1115, 1562, 1575, 1587, 2173, 3355, 3599, 3871, 4099, 4153, 4185, 4193, 4202, 4262, 4285, 4402, 4633, 4666, 6163, 6166, 6374, 9241, 9466, 16544, 16546, 16586, 16601, 16613, 16616, 16720, 16748, 16994
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Base 2 analogue of A063048 (base 10) and A075421 (base 4); subsequence of A066059. - For the trajectory of 22 (cf. A061561) and the trajectory of 77 (cf. A075253) it has been proved that they do not contain a palindrome. A similar proof can be given for most terms of this sequence, but there are a few terms (4262, 17498, 33378, 33898, ...) whose trajectory does not show the kind of regularity that can be utilized for the construction of a proof. - If the trajectory of an integer k joins the trajectory of a smaller integer which is a term of the present sequence, then this occurs after very few 'Reverse and Add!' steps (at most 84 for numbers < 20000). On the other hand, the trajectories of the terms of this sequence do not join the trajectory of any smaller term within at least 1000 steps.
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LINKS
| Klaus Brockhaus, On the 'Reverse and Add!' algorithm in base 2
Index entries for sequences related to Reverse and Add!
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EXAMPLE
| 442 is a term since the trajectory of 442 (presumably) does not lead to an integer which occurs in the trajectory of 22 or of 77.
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CROSSREFS
| Cf. A063048, A075421, A066059, A058042, A061561, A075253.
Sequence in context: A080861 A143838 A003908 * A094844 A010010 A105101
Adjacent sequences: A075249 A075250 A075251 * A075253 A075254 A075255
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KEYWORD
| base,nonn
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AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 10 2002
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