HP 12C Fibonacci Sequence

[C.Ret]

Dear friends,

Like you, my heart has fallen in love with these old machines.
But my mind remains lucid.
Why so much hassle and lines of code?

Doesn't your HP-12C have, like mine I hope, a dedicated key for calculating the elements of the Fibonacci sequence? This key is marked [FV] as Fibonacci's Value.

So you just have to properly initialize your HP-12C and it can instantly calculate any value of the Fibonacci sequence with two or three keystrokes!

For example, to obtain the value of \(F_{36}\), put the display in mode in (f)[ 0 ] to display only integers.
Enter 36, press [ n ] then [ FV ] and the value of \(F_{36}\) is displayed:


Your HP-12C can do even better and for a given element of the sequence tell you at what index it appears or at least the index of the immediate preceding element.
For example,
75025 [ FV ] [ n ] will instantly tell you that it is the 25th element!

To do this, properly initialize your HP-12C:
(f) [CLEAR FIN ]
[ 5 ] (g)[ √x ] [CHS] [1/x] [ PV ] initializes the constant factor of the Binet Formula in the Present value register PV.
[ 5 ] (g)[ √x ] [ 1 ] [ - ] [ 5 ][ 0 ][ × ][ i ] initializes the under-exponential part of the same formula in the Interest register i%.
And there is your friendly HP-12C ready to solve all your Fibonaccial worries in the same way that it allows you to solve the financial ones.

The simplified Binet Formulae is quite a build-in expression in our beloved HP-12C:
Just observe and compare the obvious: \( FV = -PV \cdot (1 + i )^n \) versus \( F_n = \frac{1}{\sqrt{5}} \left( \frac{1+\sqrt{5}}{2} \right)^n \)


Best Regards.