Let $\\varphi$ be the golden ratio: $\\varphi=\\frac{1+\\sqrt{5}}{2}.$
Remarkably it is possible to write every positive integer as a sum of powers of $\\varphi$ even if we require that every power of $\\varphi$ is used at most once in this sum.
To represent this sum of powers of $\\varphi$ we use a string of 0's and 1's with a point to indicate where the negative exponents start. We call this the representation in the phigital numberbase. So $1=1*{\\varphi}$, $2=10.01*{\\varphi}$, $3=100.01*{\\varphi}$ and $14=100100.001001*{\\varphi}$. The strings representing 1, 2 and 14 in the phigital number base are palindromic, while the string representing 3 is not. (the phigital point is not the middle character).