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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.

%I A306482 #17 Nov 21 2019 00:13:08
%S A306482 0,4,5,6,9,11,17,21,22,34,52,68,83,84,91,92,98
%N 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.
%C A306482 Record setting numbers in A306481.
%C 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.
%C A306482 Lychrel numbers in A066059; seeds in A075252 (for base 2).
%C A306482 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
%t A306482 limit = 200; (* Assumes that there is no palindrome if none is found before "limit" iterations *)
%t A306482 A066059 = Select[Range[50000],
%t A306482    Length@NestWhileList[# + IntegerReverse[#, 2] &, #, # !=
%t A306482          IntegerReverse[#, 2] &, 1, limit] == limit + 1 &];utraj = {};
%t A306482 A075252 = Select[Range[50000],    (x = NestWhileList[# + IntegerReverse[#, 2] &, #, # !=
%t A306482          IntegerReverse[#, 2] & , 1, limit];
%t A306482      If[Length@x >= limit  && Intersection[x, utraj] == {},
%t A306482       utraj = Union[utraj, x]; True,
%t A306482       utraj = Union[utraj, x]]) &];A306482 = {}; best = -1; lastj = 0;
%t A306482 utraj = {};
%t A306482 For[i = 1, i <= Length@A066059, i++,
%t A306482  For[j = lastj + 1, j <= Length@A075252, j++,
%t A306482   If[A066059[[i]] < A075252[[j]], Break[]];
%t A306482   utraj = Union[utraj, NestList[# + IntegerReverse[#, 2] &, A075252[[j]], limit]];
%t A306482   lastj = j; ];
%t A306482  l = NestWhileList[# + IntegerReverse[#, 2] &,
%t A306482    A066059[[i]], ! MemberQ[utraj, #] &, 1, limit];
%t A306482  If[Length@l == limit + 1, Continue[]];
%t A306482 If[Length@l > best, best = Length@l; AppendTo[A306482, Length@l - 1]]; ]; A306482  (* _Robert Price_, Nov 20 2019 *)
%Y A306482 Cf. A066059, A066144, A066145, A075252, A306481.
%K A306482 nonn,base,more
%O A306482 1,2
%A A306482 _A.H.M. Smeets_, Feb 18 2019