

A065198


n sets a new record for the number of 'Reverse and Add' steps needed to reach a palindrome starting with n.


32



0, 10, 19, 59, 69, 79, 89, 10548, 10677, 10833, 10911, 147996, 150296, 1000689, 1005744, 1007601, 7008899, 9008299, 100239862, 140669390, 1005499526, 10000442119, 10000761554, 10000853648, 10000973037, 10031199494, 10087799570, 1000006412206, 1090604591930, 1600005969190, 100000090745299, 100120849299260, 10000043099946481, 10078083499399210, 10442000392399960
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OFFSET

1,2


COMMENTS

Integers like 196, for which a palindrome is supposedly never reached, are of course disregarded. A065199 gives the corresponding records.
a(39) <= N = 12000700000025339936491 for which A033665(N) = 288, found on April 26, 2019 according to Doucette's web site.  M. F. Hasler, Feb 16 2020


LINKS

A.H.M. Smeets, Table of n, a(n) for n = 1..38 (terms n = 36..38 taken from Jason Doucette link below; offset adapted by Georg Fischer, Feb 17 2019)
Jason Doucette, World records
Ian J. Peter, Search for the biggest numeric palindrome, page no more available, backup on web.archive.org as of July 2011.
Index entries for sequences related to Reverse and Add!


EXAMPLE

Starting with 89, 24 'Reverse and Add' steps are needed to reach a palindrome; starting with n < 89, less (at most 6) steps are needed.


MATHEMATICA

limit = 10^3; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
best = 1; Select[Range[0, 1000], (np = #; i = 0;
While[np != IntegerReverse[np] && i < limit,
np = np + IntegerReverse[np]; i++];
If[i >= limit, False, If[i > best, best = i; True]]) &] (* Robert Price, Oct 14 2019 *)


PROG

(PARI) my(m, M=1); for(n=0, oo, if(M<m=A033665(n, M+39), print1(n", "); M=m)) \\ Only for illustration, not suitable for producing terms > 10^6, even with the custom search limit given as optional 2nd arg to A033665.  M. F. Hasler, Feb 16 2020


CROSSREFS

Cf. A033665, A033865, A023109, A065199.
Sequence in context: A219959 A307344 A330570 * A033866 A023109 A255530
Adjacent sequences: A065195 A065196 A065197 * A065199 A065200 A065201


KEYWORD

base,nonn


AUTHOR

Klaus Brockhaus, Oct 20 2001


EXTENSIONS

Terms a(17) to a(21) from Sascha Kurz, Dec 05 2001
Terms a(22) ff. were taken from Jason Doucette, World records.  Klaus Brockhaus, Sep 24 2003
Offset changed to 1 by A.H.M. Smeets, Feb 14 2019


STATUS

approved



