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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
Jason Doucette, World records
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
Sequence in context: A219048 A329577 A217442 * A249156 A033179 A067244
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
Edited by N. J. A. Sloane, Jul 16 2021
STATUS
approved

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Last modified June 21 05:50 EDT 2024. Contains 373540 sequences. (Running on oeis4.)