Algol 68 Genie

lucas-sequence.a68

     
   1  #
   2  
   3  @section Synopsis
   4  
   5  Lucas sequence and the golden ratio.
   6  
   7  The Lucas sequence has the same recursive relationship as the Fibonacci sequence. 
   8  The ratio of successive terms approaches the golden ratio, the terms themselves being 
   9  roundings of integer powers of the golden ratio. Two numbers are in the golden ratio
  10  if their ratio equals the ratio of their sum to the larger of the two numbers:
  11  
  12    (a + b) / a = a / b, with a > b > 0.
  13  
  14  #
  15  
  16  CO Using refinements CO
  17  
  18  determine first generation;
  19  WHILE can represent next generation
  20  DO calculate next generation;
  21     print next generation
  22  OD.
  23  
  24     determine first generation:
  25        LONG INT previous := 1, current := 3.
  26  
  27     can represent next generation:
  28        current <= long max int - previous.
  29  
  30     calculate next generation:
  31        LONG INT new = current + previous;
  32        previous := current;
  33        current := new.
  34  
  35     print next generation:
  36        print ((current, newline, previous, new line, current / previous, new line, new line)).

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