A348571 In Zeckendorf representation: integers that set a new record for the number of Reverse and Add steps (A349239) needed to reach a palindrome (A094202).

0, 2, 7, 20, 54, 63, 114, 1002, 1413, 3007, 4447, 35131, 599185, 2189416, 2738842, 3253273, 108250112

Offset

1,2

Comments

Corresponding record values in A348572.

For Zeckendorf representation of numbers see A014417.

Lychrel numbers, as given in A348570, are excluded from this list because it is believed that those numbers never reach a palindrome.

Links

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

A.H.M. Smeets, Python program

Example

Trajectory of 20, i.e., 101010 in Zeckendorf representation:
       101010 + 010101      =      1010100
      1010100 + 0010101     =     10010010
     10010010 + 01001001    =    100100100
    100100100 + 001001001   =   1000010001
   1000010001 + 1000100001  =  10100000010
  10100000010 + 01000000101 = 100100001001, which is palindromic.
Due to the fact that any number smaller than 20 reaches a palindrome in fewer than 6 steps, 20 is a record-setting nonnegative integer.
The Lychrel numbers, as given in A348570, are excluded, because it is believed that those numbers never reach a palindromic number.

Crossrefs

Cf. A014417 (Zeckendorf digits), A349239 (reverse and add), A094202 (palindromes).

Cf. A348572 (number of steps), A348570 (Lychrels).

Sequence in context: A096005 A050532 A050513 * A128183 A027418 A035508

Adjacent sequences: A348568 A348569 A348570 * A348572 A348573 A348574

Keyword

nonn,base,more

Author

A.H.M. Smeets, Oct 23 2021

Status

approved