2,1

It would be nice to remove the word "Conjectured" from the description - N. J. A. Sloane (njas(AT)research.att.com).

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?

Index entries for sequences related to Reverse and Add!

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

Sequence in context: A044654 A156795 A095265 this_sequence A124950 A126409 A041938

Adjacent sequences: A066447 A066448 A066449 this_sequence A066451 A066452 A066453

nonn

Frederick Magata (frederick.magata(AT)t-online.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.