A065320 53 'Reverse and Add' steps are needed to reach a palindrome.

10677, 11667, 12657, 13647, 14637, 15627, 16617, 17607, 20676, 21666, 22656, 23646, 24636, 25626, 26616, 27606, 30675, 31665, 32655, 33645, 34635, 35625, 36615, 37605, 40674, 41664, 42654, 43644, 44634, 45624, 46614, 47604, 50673

Offset: 1

Author

Klaus Brockhaus, Oct 30 2001

Keywords

• nonn
• base

Comments

The number of steps starts at 0, so palindromes (cf. A002113) are excluded. 53 is a record (cf. A065199) of the number of 'Reverse and Add' steps needed to reach a palindrome.

The first term not congruent 84 mod 99 is a(64) = 109902, thereafter the residues show no obvious pattern. - Klaus Brockhaus, Jul 14 2003

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..67
• Index entries for sequences related to Reverse and Add!

Crossrefs

Cf. A002113, A065198, A065199, A065318.

Programs

Mathematica

lenQ[n_]:= Length[NestWhileList[# + FromDigits[Reverse[IntegerDigits[#]]]&, n, #! = FromDigits[Reverse[IntegerDigits[#]]]&, 1, 54]] == 54; Select[Range[10000], lenQ] (* Vincenzo Librandi, Sep 24 2013 *)

Extensions

Changed offset from 0 to 1 by Vincenzo Librandi, Sep 24 2013