A306482 Records for the number of 'Reverse and Add' steps in base 2 needed for a Lychrel number to join the trajectory of a smaller Lychrel number (i.e., its seed). Record setting numbers in A306481.

0, 4, 5, 6, 9, 11, 17, 21, 22, 34, 52, 68, 83, 84, 91, 92, 98

Offset: 1

Author

A.H.M. Smeets, Feb 18 2019

Keywords

• nonn
• base
• more

Comments

Record setting numbers in A306481.

Similar to the number of steps needed to reach a palindrome in the Reverse and Add! trajectories (see A066144 and A066145), the number of steps needed for a Lychrel number to reach the trajectory of its seed is relatively small.

Lychrel numbers in A066059; seeds in A075252 (for base 2).

As a clarification, this sequence can also be described as: "Records for the number of 'Reverse and Add' steps in base 2 needed for a base 2 Lychrel number (A066059) to join the trajectory of a smaller base 2 Lychrel number seed (A075252)." - Robert Price, Nov 20 2019

Crossrefs

Cf. A066059, A066144, A066145, A075252, A306481.

Programs

Mathematica

limit = 200; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
A066059 = Select[Range[50000],
   Length@NestWhileList[# + IntegerReverse[#, 2] &, #, # !=
         IntegerReverse[#, 2] &, 1, limit] == limit + 1 &];utraj = {};
A075252 = Select[Range[50000],    (x = NestWhileList[# + IntegerReverse[#, 2] &, #, # !=
         IntegerReverse[#, 2] & , 1, limit];
     If[Length@x >= limit  && Intersection[x, utraj] == {},
      utraj = Union[utraj, x]; True,
      utraj = Union[utraj, x]]) &];A306482 = {}; best = -1; lastj = 0;
utraj = {};
For[i = 1, i <= Length@A066059, i++,
 For[j = lastj + 1, j <= Length@A075252, j++,
  If[A066059[[i]] < A075252[[j]], Break[]];
  utraj = Union[utraj, NestList[# + IntegerReverse[#, 2] &, A075252[[j]], limit]];
  lastj = j; ];
 l = NestWhileList[# + IntegerReverse[#, 2] &,
   A066059[[i]], ! MemberQ[utraj, #] &, 1, limit];
 If[Length@l == limit + 1, Continue[]];
If[Length@l > best, best = Length@l; AppendTo[A306482, Length@l - 1]]; ]; A306482  (* Robert Price, Nov 20 2019 *)