(41) Fibonacci Decomposition (integer)

[Thomas Klemm]

This shorter program for the HP-42S may take a bit longer especially for bigger numbers:

Code:

00 { 27-Byte Prgm }
01▸LBL "FNS"
02 0
03 X<>Y
04 1
05▸LBL 00
06 X>Y?
07 GTO 01
08 STO+ ST Z
09 X<> ST Z
10 GTO 00
11▸LBL 01
12 R↓
13 RCL- ST Y
14 END

It should work with the HP-41C as well after the obvious transformations.
You may want to add a VIEW Y command at the end.

Examples

65 XEQ "FNS"

y: 55
x: 10

R/S

y: 8
x: 2

R/S

y: 2
x: 0

Therefore: \(65 = 55 + 8 + 2\)


1000 XEQ "FNS"

y: 987
x: 13

R/S

y: 13
x: 0

Therefore: \(1000 = 987 + 13\)

References

• Fibonacci coding