Recamán's Sequence - Musical Mathematical Visualization | 8gwifi.org

🎵 Recamán's Sequence 🎵

Explore the beautiful mathematical sequence with musical patterns

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🧠 Recamán's Sequence Explained

Recamán's Sequence is a mathematical sequence defined by the Colombian mathematician Bernardo Recamán Santos.

Definition:

  • Start with a(0) = 0
  • For n > 0: a(n) = a(n-1) - n if positive and not already in sequence
  • Otherwise: a(n) = a(n-1) + n

Fascinating Properties:

  • The sequence creates beautiful arcs when visualized
  • It can be mapped to musical notes, creating interesting patterns
  • The sequence contains many unanswered mathematical questions
  • It's unknown whether every positive integer appears in the sequence

Visualization: When plotted, the sequence creates arcs that bounce back and forth, creating a mesmerizing pattern that resembles sound waves or musical notation!

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