(41) Fibonacci and Lucas Numbers

[SlideRule]

from Number Theory in Science and Communication, M.R. Schroeder, second enlarged edition, Springer-Verlag {pgs. 345-346}

PHP Code:

B.  A Calculator Program for Calculating Fibonacci and Lucas Numbers

To call the program, which is labeled "FN", from storage, press
     GTO "FN"
To calculate, for example, the 12th Fibonacci number, F12, press
     12
     R/S
After about 1 second one sees the answer:
    144,
with a comma at the end.  Pressing
     R/S
again gives the 12th Lucas number, L12:
     322 .
with a period at the end (to distinguish it from the Fibonacci number and to
tell the user that the calculator is ready to accept the next index). The
calculator is accurate up to F39 and L37 .
Pressing the multiplication sign yields
     F2n = Fn . Ln = 46368 (for n = 12) .
This rule comes in handy to calculate Fn for large even n.
     The odd-index Fn are calculated by
     F2n+ I  = gF2n  = 75025  (for n = 12) ,
where g  = 1.618 … is the Golden ratio, stored in register 02.
                Listing for "FN"
___________________________________________
Comment                      Step Code
___________________________________________
initialize by calculating    01    LBL "FN"
                             02    5
                             03    SQRT
√5                           04    STO 01
                             05    1
                             06    +
                             07    0.5
                             08    •
Golden ratio                 09    STO 02
                             10    RDN
subroutine for calculat-     11    LBL 11
ing Fn and Ln                12    RCL 02
                             13    x < > Y
                             14    y^x
                             15    STO 03
                             16    RCL 01
                             17    /
                             18    0.5
                             19    +
                             20    INT
                             21    FIX 0
                             22    CF 28
display Fn                   23    STOP
                             24    RCL 03
                             25    0.5
                             26    +
                             27    INT
                             28    SF 28
display Ln                   29    STOP
ready to start over          30    GTO 11
                             31    END 


real gems are yet to be revealed from 'obscure' sources.

BEST!
SlideRule

ps: follow-on to this thread, HP-41 Modulo function, in the General Forum HP Calculators (and very old HP Computers)