Phigital number base
Problem 473
Let be the golden ratio:
Remarkably it is possible to write every positive integer as a sum of powers of even if we require that every power of is used at most once in this sum.
Even then this representation is not unique.
We can make it unique by requiring that no powers with consecutive exponents are used and that the representation is finite.
E.g: and
Remarkably it is possible to write every positive integer as a sum of powers of even if we require that every power of is used at most once in this sum.
Even then this representation is not unique.
We can make it unique by requiring that no powers with consecutive exponents are used and that the representation is finite.
E.g: and
To represent this sum of powers of 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 , , and .
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).
We call this the representation in the phigital numberbase.
So , , and .
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).
The sum of the positive integers not exceeding 1000 whose phigital representation is palindromic is 4345.
Find the sum of the positive integers not exceeding whose phigital representation is palindromic.