

A065199


Record high values in A033665, ignoring those numbers that are believed never to reach a palindrome.


34



0, 1, 2, 3, 4, 6, 24, 30, 53, 54, 55, 58, 64, 78, 79, 80, 82, 96, 97, 98, 109, 112, 113, 131, 135, 147, 149, 186, 187, 188, 198, 201, 232, 233, 236, 259, 260, 261
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

Records for the number of 'Reverse and Add' steps needed to reach a palindrome.
A065198 gives the corresponding starting points.


LINKS



FORMULA



EXAMPLE

Starting with 89, 24 'Reverse and Add' steps are needed to reach a palindrome; starting with n < 89, at most 6 steps are needed.
For n = A065198(21) = 1005499526, a(21) = 109 "reverse and add" operations are needed to reach a palindrome; for all smaller n, at most 98 steps are needed.
For n = A065198(31) ~ 10^14, a(31) = 198 "reverse and add" operations are needed to reach a palindrome; for all smaller n, at most 188 steps are needed.
For n = A065198(36) ~ 10^18, a(36) = 259 "reverse and add" operations are needed to reach a palindrome; for all smaller n, at most 236 steps are needed.


MATHEMATICA

limit = 10^3; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
best = 1; lst = {};
For[n = 0, n <= 100000, n++,
np = n; i = 0;
While[np != IntegerReverse[np] && i < limit,
np = np + IntegerReverse[np]; i++];
If[i < limit && i > best, best = i; AppendTo[lst, i]]]; lst (* Robert Price, Oct 14 2019 *)


PROG

(PARI) my(m, M=1); for(n=0, oo, (M<m=A033665(n, M+39))&&print1(M=m", ")) \\ For illustration; becomes very slow for terms > 70, even with the "custom" search limit as optional 2nd arg to A033665.  M. F. Hasler, Feb 16 2020


CROSSREFS



KEYWORD

base,nonn,hard


AUTHOR



EXTENSIONS

Terms a(22) onwards were taken from Jason Doucette, World records.  Klaus Brockhaus, Sep 24 2003
Terms a(36) to a(38) were taken from Jason Doucette, World records and added by A.H.M. Smeets, Feb 10 2019


STATUS

approved



