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A066450 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.

%I A066450 #30 Mar 07 2022 03:15:39
%S A066450 22,103,290,708,1079,2656,1021,593,196,1011,237,2701,361,447,413,3297,
%T A066450 519,341,379,711,461,505,551,1022,649,701,755,811,869,929,991,1055,
%U A066450 1799,1922,1259,1331,1405,1481,1559,1639,1595,1762,1891,1934,2069,2161
%N A066450 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.
%C A066450 It would be nice to remove the word "Conjectured" from the description. - _N. J. A. Sloane_
%C A066450 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.)
%C A066450 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.
%C A066450 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?
%H A066450 Klaus Brockhaus, <a href="/A058042/a058042.txt">On the 'Reverse and Add!' algorithm in base 2</a>
%H A066450 T. Irvin, <a href="http://www.fourmilab.ch/documents/threeyears/two_months_more.html">About Two Months of Computing, or An Addendum to Mr. Walker's Three Years of Computing. </a>
%H A066450 J. Walker, <a href="http://www.fourmilab.ch/documents/threeyears/threeyears.html">Three Years Of Computing: Final Report On The Palindrome Quest</a>
%H A066450 <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>
%t A066450 limit = 10^3; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
%t A066450 Table[SelectFirst[Range[10000],
%t A066450   Length@NestWhileList[ # + IntegerReverse[#, n] &,  #, # !=
%t A066450         IntegerReverse[#, n]  &, 1, limit] == limit + 1 &] , {n, 2,
%t A066450 47}] (* _Robert Price_, Oct 18 2019 *)
%K A066450 nonn,base
%O A066450 2,1
%A A066450 Frederick Magata (frederick.magata(AT)uni-muenster.de), Dec 29 2001
%E A066450 _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.