OFFSET
1,2
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.
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
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++,
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 *)
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
A.H.M. Smeets, Feb 18 2019
STATUS
approved