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 A066450 Conjectured values for the minimal number a(n) such that 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. 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS 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? LINKS Klaus Brockhaus, On the 'Reverse and Add!' algorithm in base 2 MATHEMATICA 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, 47}] (* Robert Price, Oct 18 2019 *) CROSSREFS Sequence in context: A156795 A095265 A060382 * A231225 A124950 A126409 Adjacent sequences:  A066447 A066448 A066449 * A066451 A066452 A066453 KEYWORD nonn,base AUTHOR Frederick Magata (frederick.magata(AT)uni-muenster.de), Dec 29 2001 EXTENSIONS 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. STATUS approved

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Last modified August 5 07:33 EDT 2020. Contains 336209 sequences. (Running on oeis4.)