A348571 - OEIS

%I #40 Dec 13 2021 17:01:01

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

%T 3253273,108250112

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

%C Corresponding record values in A348572.

%C For Zeckendorf representation of numbers see A014417.

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

%H A.H.M. Smeets, <a href="/A348572/a348572_1.txt">Python program</a>

%e Trajectory of 20, i.e., 101010 in Zeckendorf representation:

%e        101010 + 010101      =      1010100

%e       1010100 + 0010101     =     10010010

%e      10010010 + 01001001    =    100100100

%e     100100100 + 001001001   =   1000010001

%e    1000010001 + 1000100001  =  10100000010

%e   10100000010 + 01000000101 = 100100001001, which is palindromic.

%e 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.

%e The Lychrel numbers, as given in A348570, are excluded, because it is believed that those numbers never reach a palindromic number.

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

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

%K nonn,base,more

%O 1,2

%A _A.H.M. Smeets_, Oct 23 2021