A306481 Lychrel numbers k that set a new record for the number of 'Reverse and Add' steps in base 2 needed to reach a Lychrel number m < k (i.e., its seed).

22, 26, 67, 106, 157, 199, 281, 1145, 1594, 1798, 4326, 12794, 17407, 18428, 67583, 69628, 73978

Offset: 1

Author

A.H.M. Smeets, Feb 18 2019

Keywords

• nonn
• base
• more

Comments

Records in A306482.

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: Base 2 Lychrel numbers (A066059) k that sets a new record for the number of 'Reverse and Add' steps in base 2 needed to reach the trajectory of a base 2 Lychrel number seed (A075252) that is less than k. - Robert Price, Nov 20 2019

Crossrefs

Cf. A066059, A066144, A066145, A075252, A306482.

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]]) &];
A306481 = {}; 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[A306481, A066059[[i]]]];
]; A306481 (* Robert Price, Nov 20 2019 *)