Fibonacci Sequence and Selfie Numbers

I came across a useful 47 page resource titled Fibonacci Sequence and Selfie Numbers when searching for properties associated with 27451, the number representing how old I am today in days. The article begins as follows:

Numbers represented by their own digits by certain operations are considered as ”Selfie Numbers”. There are many ways of representing ”Selfie Numbers”, such as, numbers written in digit’s order or its reverse. It can also be represented in increasing and/or decreasing order of digits. This is generally obtained by use of basis operations along with factorial and square-root, etc. In this work we have written ”Selfie Numbers” using Fibonacci sequence value in composition form in terms of digit’s order and its reverse.

So for 27451 if we take the digits in order and use F(n) to represent the n-th Fibonacci number than we can write it as F(2 + F(7)) × 45 + 1. In fact, 27451 is one of a group of numbers that can be represented in this way. See Figure 1.

Figure 1

Numbers that can be represented in this way are not that frequent. The next group is shown in Figure 2.

Figure 2

After this the next group does not occur until 43460. Some numbers can be represented in terms of their digit order and the reverse. See Figure 3.

Figure 3

All in all, a useful resource and I've uploaded the PDF to my Google Drive where I can access it whenever I'm struggling to find an interesting property for a number associated with my diurnal age. The author of this paper is absolutely prolific and has published many other papers as well. These are listed in the article and one example is a 55 page paper titled Single Digit Representations of Natural Numbers. The abstract is as follows:

In this work, we established symmetric representation of numbers where one can use any of 9 digits giving the same number. The representations of natural numbers from 0 to 1000 are given using only single digit in all the nine cases, i.e., 1, 2, 3, 4, 5, 6, 7, 8 and 9. This is done only using basic operations: addition, subtraction, multiplication, potentiation and division.

For example, 37 can be written as:$$ \begin{align} 37 &= \frac{111}{1+1+1}\\ &=\frac{222}{2+2+2} \\ &= \frac{333}{3+3+3} \text{ etc.} \end{align}$$Overall, this author's papers seem ideally suited to my Number Theory needs and I'll download them all and add them to my Google Drive for easy access in the future.