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A066450
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a(n) is the conjectured value of the minimal number to which repeated application of the "reverse and add!" algorithm in base n does not terminate in a palindrome. If there is no such number in base n, then a(n) := -1.
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4
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22, 103, 290, 708, 1079, 2656, 1021, 593, 196, 1011, 237, 2701, 361, 447, 413, 3297, 519, 341, 379, 711, 461, 505, 551, 1022, 649, 701, 755, 811, 869, 929, 991, 1055, 1799, 1922, 1259, 1331, 1405, 1481, 1559, 1639, 1595, 1762, 1891, 1934, 2069, 2161
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OFFSET
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2,1
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COMMENTS
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It would be nice to remove the word "Conjectured" from the description. - N. J. A. Sloane
All the terms in this sequence except the first are only conjectures. (See Walker, Irvin on a(10)=196 and Brockhaus on a(2)=22.)
An obvious algorithm is: start with r := n and check whether the "reverse and add!" algorithm in base n halts in a palindrome or not. If it stops, increment r by one and repeat the process, else return r. To obtain the values above, an upper limit of 100 "reverse and add!" steps was used.
Conjectures: a(n) shows the same asymptotic behavior as n^2. For infinitely many n, a(n) = n^2 - n - 1. Again, it is an open question, if the values of the sequence really lead to infinitely many "reverse and add!" steps or not. Is the sequence always positive?
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LINKS
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MATHEMATICA
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limit = 10^3; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
Table[SelectFirst[Range[10000],
Length@NestWhileList[ # + IntegerReverse[#, n] &, #, # !=
IntegerReverse[#, n] &, 1, limit] == limit + 1 &] , {n, 2,
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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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Frederick Magata (frederick.magata(AT)uni-muenster.de), Dec 29 2001
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EXTENSIONS
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David W. Wilson remarks (Jan 02 2002): I verified these using 1000 digits as a stopping point (this would be >>1000 iterations). I am highly confident of these values.
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STATUS
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approved
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