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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)



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?


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!


Sequence in context: A044654 A156795 A095265 * A231225 A124950 A126409

Adjacent sequences:  A066447 A066448 A066449 * A066451 A066452 A066453




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


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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Last modified March 23 17:19 EDT 2019. Contains 321432 sequences. (Running on oeis4.)