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algorithmuscanorj

About relationship between this sequence and A030298

Dec 28th, 2012
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  1. Interesting property identified for the pair of sequences A207324 and A030298:
  2.  
  3. Since both sequences are based on particular ways of reading permutations, we may
  4. expect to find similarities among its terms.
  5.  
  6. The first 105 terms for A207324 are (without commas):
  7.  
  8. 112211231323123212312131234124314234123413214321342132431243142341243124321342132413214231423412431423142
  9.  
  10. The same quantity of terms found for A030298 when visited (at least on Sat, Sept 15th 2012 at 19:04 VET) are:
  11.  
  12. 112211231322132313123211234124313241342142314322134214323142341241324313124314232143241341234214123413242
  13.  
  14. Placing these rows closer and comparing:
  15. 112211231323123212312131234124314234123413214321342132431243142341243124321342132413214231423412431423142
  16. 112211231322132313123211234124313241342142314322134214323142341241324313124314232143241341234214123413242
  17.  
  18. We may compare the equality of corresponding columns by offset from left to right, finding a pattern:
  19.  
  20. yyyyyyyyyyyyyyyyyNNNNNNyyyyyyyyyNNNNNNNNNNNyyyyNNNNNNNNNNNyNNyNNyyNNNNNNNyNyNNNyyNNyyNNNNyNNNNyNNNNyNyNyy
  21. 111111111111111110000001111111110000000000011110000000000010010011000000010100011001100001000010000101011
  22.  
  23. Which may be called the answer pattern for the question: Are the columns values identical?, made 105 times,
  24. one time per column.
  25.  
  26. But the equality isn't the unique question we may propose as criteria for building the pattern.
  27. Another interesting questions all of them of course matter of comparison, are:
  28.  
  29. -Are both values (top and bottom) prime numbers?
  30. -Are both values (top and bottom) odd numbers?
  31. -Are both values (top and bottom) even numbers?
  32. -Are both values (top and bottom) perfect numbers?
  33. -Are both values (top and bottom) Mersenne numbers?
  34. -Are both values (top and bottom) Mersenne primes?
  35. -Does both values sum a prime number?
  36. -Are one of these values some integer power or exact root respect the other?
  37. -Have these values an integer (arithmetical) average?
  38. -Have these values an odd or even GCD?
  39.  
  40. An extra conceptual dimen could be added if we consider as the value on a new sequence associated with a given offset
  41. the decimal number for the binary digits pattern built based on some kind of comparison where the offset consists
  42. of how many terms are picked and from each one A207324 and A030298 for comparison.
  43.  
  44. Then, there is a lot of interesting sequences which one may think to build.
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