 As with base-φ, the digit sequence "11" is avoided by rearranging to a standard form, using the Fibonacci recurrence relation "F""k"+1 = "F""k" + "F""k"−1.For example,

It is possible to mix base-φ arithmetic with Fibonacci integer sequences.The sum of numbers in a General Fibonacci integer sequence that correspond with the nonzero digits in the base-φ number, is the multiplication of the base-φ number and the element at the zero-position in the sequence.