%I #30 Mar 07 2022 03:15:39

%S 22,103,290,708,1079,2656,1021,593,196,1011,237,2701,361,447,413,3297,

%T 519,341,379,711,461,505,551,1022,649,701,755,811,869,929,991,1055,

%U 1799,1922,1259,1331,1405,1481,1559,1639,1595,1762,1891,1934,2069,2161

%N 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 It would be nice to remove the word "Conjectured" from the description. - _N. J. A. Sloane_

%C 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 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 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 Klaus Brockhaus, <a href="/A058042/a058042.txt">On the 'Reverse and Add!' algorithm in base 2</a>

%H 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 J. Walker, <a href="http://www.fourmilab.ch/documents/threeyears/threeyears.html">Three Years Of Computing: Final Report On The Palindrome Quest</a>

%H <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>

%t limit = 10^3; (* Assumes that there is no palindrome if none is found before "limit" iterations *)

%t Table[SelectFirst[Range[10000],

%t Length@NestWhileList[ # + IntegerReverse[#, n] &, #, # !=

%t IntegerReverse[#, n] &, 1, limit] == limit + 1 &] , {n, 2,

%t 47}] (* _Robert Price_, Oct 18 2019 *)

%K nonn,base

%O 2,1

%A Frederick Magata (frederick.magata(AT)uni-muenster.de), Dec 29 2001

%E _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.