

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
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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

Table of n, a(n) for n=2..47.
Klaus Brockhaus, On the 'Reverse and Add!' algorithm in base 2
T. Irvin, About Two Months of Computing, or An Addendum to Mr. Walker's Three Years of Computing.
J. Walker, Three Years Of Computing: Final Report On The Palindrome Quest
Index entries for sequences related to Reverse and Add!


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)unimuenster.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



