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

1,2

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)

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!

Example

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.

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: A307344 A330570 A369305 * 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

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

Status

approved