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%I #65 Dec 23 2021 02:26:18
%S 0,10,19,59,69,79,89,10548,10677,10833,10911,147996,150296,1000689,
%T 1005744,1007601,7008899,9008299,100239862,140669390,1005499526,
%U 10000442119,10000761554,10000853648,10000973037,10031199494,10087799570,1000006412206,1090604591930,1600005969190,100000090745299,100120849299260,10000043099946481,10078083499399210,10442000392399960
%N Indices of record high values in A033665, ignoring those numbers that are believed never to reach a palindrome.
%C Integers like 196, for which a palindrome is supposedly never reached, are disregarded. A065199 gives the corresponding records.
%C 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
%C From _A.H.M. Smeets_, Sep 18 2021: (Start)
%C Let d_0 d_1 d_2 ... d_n be the decimal digits of an (n+1)-digit number.
%C All numbers in this sequence seem to satisfy the following condition:
%C d_0 = "1" or d_n = "9", and for all k, 0 < k < floor((n-1)/2), d_k = "0" or d_k = "9" or d_(n-k) = "0" or d_(n-k) = "9".
%C As from this, N = 12000700000025339936491, does not seem to be a record-setting number in this sequence, i.e., there must exist a smaller number N with at least a delay of 288 to reach a palindromic number. (End)
%H A.H.M. Smeets, <a href="/A065198/b065198.txt">Table of n, a(n) for n = 1..38</a> (terms n = 36..38 taken from Jason Doucette link below; offset adapted by _Georg Fischer_, Feb 17 2019)
%H Jason Doucette, <a href="http://www.jasondoucette.com/worldrecords.html">World records</a>
%H Ian J. Peter, <a href="https://web.archive.org/web/20110728141429/http://www.floot.demon.co.uk/palindromes.html">Search for the biggest numeric palindrome</a>, lost page, pointer to backup on web.archive.org as of July 2011.
%H <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>
%e Starting with 89, 24 'Reverse and Add' steps are needed to reach a palindrome; starting with n < 89, fewer (at most 6, in fact) steps are needed. So 89 is a term.
%t limit = 10^3; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
%t best = -1; Select[Range[0, 1000], (np = #; i = 0;
%t While[np != IntegerReverse[np] && i < limit,
%t np = np + IntegerReverse[np]; i++];
%t If[i >= limit, False, If[i > best, best = i; True]]) &] (* _Robert Price_, Oct 14 2019 *)
%o (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
%Y Cf. A033665, A033865, A023109, A065199.
%K base,nonn
%O 1,2
%A _Klaus Brockhaus_, Oct 20 2001
%E Terms a(17) to a(21) from _Sascha Kurz_, Dec 05 2001
%E Terms a(22) ff. were taken from Jason Doucette, World records. - _Klaus Brockhaus_, Sep 24 2003
%E Offset changed to 1 by _A.H.M. Smeets_, Feb 14 2019
%E Edited by _N. J. A. Sloane_, Jul 16 2021
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