A348570 -id:A348570 - cp's OEIS frontend

A349239 a(n) = n + (reversal of digits in the Zeckendorf representation of n).

0, 2, 3, 4, 8, 6, 12, 11, 9, 18, 16, 15, 24, 14, 28, 24, 22, 36, 22, 36, 32, 22, 44, 37, 33, 55, 32, 54, 47, 33, 55, 48, 44, 66, 35, 70, 58, 51, 86, 48, 83, 71, 48, 83, 71, 64, 99, 51, 86, 74, 67, 102, 64, 99, 87, 56, 112, 92, 80, 136, 74, 130, 110, 72, 128, 108

Offset: 0

Kevin Ryde, Nov 11 2021

Kevin Ryde, Table of n, a(n) for n = 0..10000
Kevin Ryde, PARI/GP Code

Cf. A189920 (Zeckendorf digits), A349238 (reverse), A349240 (reverse and subtract), A348570 (Lychrels).

Other bases: A055944 (binary), A056964 (decimal).

PARI
```
\\ See links.
```

# Using functions NumToFib and RevFibToNum from A349238.
n, a = 0, 0
print(a + a, end = ", ")
while n < 65:
    n += 1
    print(n + RevFibToNum(NumToFib(n)), end = ", ") # A.H.M. Smeets, Nov 14 2021

a(n) = n + A349238(n).

a(n) = 2*n - A349240(n).

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).

Original entry on oeis.org

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

Offset: 1

A.H.M. Smeets, Oct 23 2021

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.

			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.

A.H.M. Smeets, Python program

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

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

cp's OEIS Frontend

A349239 a(n) = n + (reversal of digits in the Zeckendorf representation of n).

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