A306481 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

LINKS

Table of n, a(n) for n=1..17.

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 *)

CROSSREFS

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

Sequence in context: A277624 A243140 A321996 * A211320 A215601 A172053

Adjacent sequences: A306478 A306479 A306480 * A306482 A306483 A306484

KEYWORD

nonn,base,more

AUTHOR

A.H.M. Smeets, Feb 18 2019

STATUS

approved