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Search: id:A023108
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| A023108 |
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Positive integers which apparently never result in a palindrome under repeated applications of the function f(x) = x + (x with digits reversed). |
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+0
56
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| 196, 295, 394, 493, 592, 689, 691, 788, 790, 879, 887, 978, 986, 1495, 1497, 1585, 1587, 1675, 1677, 1765, 1767, 1855, 1857, 1945, 1947, 1997, 2494, 2496, 2584, 2586, 2674, 2676, 2764, 2766, 2854, 2856, 2944, 2946, 2996, 3493, 3495, 3583, 3585, 3673, 3675
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Also called Lychrel numbers.
The definition of "Lychrel number" varies: Purists only call the "seeds" or "root numbers" Lychrel; the "related" or "extra" numbers (arising in the former's orbit) have been coined "Kin numbers" by Koji Yamashita. There are only 2 "root" Lycherels below 1000 and 3 more below 10000, cf. A088753. - M. F. Hasler, Dec 04 2007
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REFERENCES
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F. Gruenberger, Computer Recreations, Scientific American, 250 (No. 4, 1984), 19-26.
R. K. Guy, What's left?, preprint, 1998.
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LINKS
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P. De Geest, Some thematic websources
Jason Doucette, World Records
T. Irvin, About Two Months of Computing, or An Addendum to Mr. Walker's Three Years of Computing
N. N., www.p196.org
Project Euler, Problem 55: How many Lychrel numbers are there below ten-thousand?
Wade VanLandingham, Largest known Lychrel number
J. Walker, Three Years Of Computing: Final Report On The Palindrome Quest
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, 196-Algorithm
Eric Weisstein's World of Mathematics, Lychrel Number
Index entries for sequences related to Reverse and Add!
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CROSSREFS
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Cf. A006960, A088753, A063048, A089694, A089521.
Adjacent sequences: A023105 A023106 A023107 this_sequence A023109 A023110 A023111
Sequence in context: A151713 A118781 A119667 this_sequence A092231 A089493 A088753
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KEYWORD
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nonn,base,nice
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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196 is conjectured to be smallest initial term which does not lead to a palindrome. John Walker, Tim Irvin and others have extended this to millions of digits without finding one.
Edited by M. F. Hasler (maximilian.hasler(AT)gmail.com), Dec 04 2007
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