A065199 Record high values in A033665, ignoring those numbers that are believed never to reach a palindrome.

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

Offset: 1

Author

Klaus Brockhaus, Oct 20 2001

Keywords

• base
• nonn
• hard

Comments

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

A065198 gives the corresponding starting points.

Examples

			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.
		

Links

• Jason Doucette, World records
• Index entries for sequences related to Reverse and Add!

Crossrefs

Cf. A033665, A033865, A023109, A065198.

Programs

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 *)

PARI

my(m, M=-1); for(n=0, oo, (MA033665(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

Formula

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

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

Edited by N. J. A. Sloane, Jul 16 2021