jlpe's number recreations page

The concept of number is the obvious distinction between the beast and man. Thanks to number, the cry becomes song, noise acquires rhythm, the spring is transformed into a dance, force becomes dynamic, and outlines figures.

Joseph Marie de Maistre

I have hardly ever known a mathematician who was capable of reasoning.

Plato

  1. On a Generalization of Perfect Numbers
  2. Ana's Golden Fractal
  3. The 3x + 1 Fractal
  4. The Picture-Perfect Numbers
  5. Fractal Dimension, Primes, and the Persistence of Memory
  6. A Miscellany of Abundant Number Problems
  7. A Tough(?) Sequence Convergence Problem
  8. The Tcefrep and Anti-Perfect Numbers
  9. Successive Absolute Differences from Squares of Primes
  10. A Conjecture on Iterates of Euler's Phi Function
  11. Prime Gap Tug of War
  12. Pointer Primes
  13. The Highly-Imperfect Numbers
  14. Solving Omega Recurrences
  15. Does the Intensity of Binary Audioactive Decay Converge?
  16. Does Sum_{i} 1/LookAndSay(prime(i)) Converge?
  17. The Audio-Prime Numbers
  18. Apexes and Nadirs of Arithmetical Functions
  19. A Conjecture on a Problem of Carmichael
  20. A Problem on C(2n,n)+n+1
  21. A Problem on Sigma and Antisigma
  22. The Enlightened Numbers
  23. The Didactic (or Sensei) Numbers
  24. On Approximate Harmonic Division of n by phi(n)
  25. On Solutions of phi(n) = phi(n-1) + phi(n-2)
  26. Fixated Points of Arithmetical Functions
  27. Palinpoints of Arithmetical Functions
  28. The Fibonacci Mirror Sequence
  29. Can a Prime Number Count?
  30. On Omega Numbers and the Omniscience of Pi
  31. Domino Games on Integer Sequences
  32. A Numerical Axis of Evil
  33. The Prime-Perfect Numbers
  34. Trying to Write e as a Concatenation of Primes
  35. Sigma(n) as a Non-trivial Power
  36. The Euler Phibonacci Sequence
  37. The Justice of Numbers

Disclaimer: The author will not be responsible for any frustration or sleepless nights suffered by the would-be solver.

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© 2001-2008. Recreations by J. L. Pe Last update: 1 May 2008. 1