

A065199


Records for the number of 'Reverse and Add' steps needed to reach a palindrome.


31



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
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OFFSET

1,3


COMMENTS

A065198 gives the corresponding starting points.


LINKS

Table of n, a(n) for n=1..38.
Jason Doucette, World records
Index entries for sequences related to Reverse and Add!


FORMULA

a(n) = A033665(A065198(n)).  M. F. Hasler, Feb 16 2020


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

Cf. A033665, A033865, A023109, A065198.
Sequence in context: A219048 A329577 A217442 * A249156 A033179 A067244
Adjacent sequences: A065196 A065197 A065198 * A065200 A065201 A065202


KEYWORD

base,nonn,hard


AUTHOR

Klaus Brockhaus, Oct 20 2001


EXTENSIONS

Terms a(17) to a(21) from Sascha Kurz, Dec 05 2001
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



