A065198 Indices of record high values in A033665, ignoring those numbers that are believed never to reach a palindrome.

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

Offset: 1

Author

Klaus Brockhaus, Oct 20 2001

Keywords

• base
• nonn

Comments

Integers like 196, for which a palindrome is supposedly never reached, are 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

From A.H.M. Smeets, Sep 18 2021: (Start)

Let d_0 d_1 d_2 ... d_n be the decimal digits of an (n+1)-digit number.

All numbers in this sequence seem to satisfy the following condition:

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".

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)

Examples

			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.
		

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, lost page, pointer to backup on web.archive.org as of July 2011.
• Index entries for sequences related to Reverse and Add!

Crossrefs

Cf. A033665, A033865, A023109, A065199.

Programs

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 *)

PARI

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

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

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