RPN HP 12C: Fibonacci and Lucas Sequences
Golden Ratio, Formulas, and Sequences
Let φ be the Golden Ratio:
φ = (1 + √5) ÷ 2
Formulas and Sequences
Fibonacci Numbers:
Fn = (φ^n - (-φ)^-n) ÷ √5
F0 = 0
F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
F6 = 8
F7 = 13
F8 = 21
F9 = 34
F10 = 55
Lucas Numbers:
Ln = φ^n + (-1)^n × (1 ÷ φ^n)
P0 = 2
P1 = 1
P2 = 3
P3 = 4
P4 = 7
P5 = 11
P6 = 18
P7 = 29
P8 = 47
P9 = 76
P10 = 123
HP 12C Code: Fibonacci and Lucas Numbers
Stack: X: n
01:[ 44, 1]: STO 1
02:[ 1]: 1
03:[ 44, 0]: STO 0
04:[ 5]: 5
05:[ 43, 21]: √
06:[44, 40, 0]: STO+ 0
07:[ 2]: 2
08:[44, 10, 0]: STO÷ 0 // Golden Ratio
09:[ 45, 0]: RCL 0
10:[ 45, 1]: RCL 1
11:[ 21]: y^x
12:[ 44, 2]: STO 2
13:[ 44, 3]: STO 3
14:[ 45, 0]: RCL 0
15:[ 16]: CHS
16:[ 45, 1]: RCL 1
17:[ 16]: CHS
18:[ 21]: y^x
19:[44, 30, 2]: STO- 2
20:[ 5]: 5
21:[ 43, 21]: √
22:[44, 10, 2]: STO÷ 2
23:[ 45, 2]: RCL 2
24:[ 31]: R/S // Fibonacci Numbers
25:[ 1]: 1
26:[ 16]: CHS
27:[ 45, 1]: RCL 1
28:[ 21]: y^x
29:[ 45, 3]: RCL 3
30:[ 22]: 1/x
31:[ 20]: ×
32:[44, 40, 3]: STO+ 3
33:[ 45, 3]: RCL 3
34:[43, 33, 00]: GTO 00
Variables:
R0 = φ
R1 = n
R2 = Fn
R3 = Ln
Sources
"Generalizations of Fibonacci numbers". Wikipedia. https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Fibonacci_integer_sequences Last Edited October 6, 2024. Accessed June 18, 2025
Olson, Scott. The Golden Section: Nature Greatest Secret. Wooden Books. Bloomsbury. New York, NY and London, UK. 2006. ISBN 978-0-8027-1539-5
Eddie
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