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home_primes.sf

home_primes.sf 2.0 KB
Cronologia Originale

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  1. #!/usr/bin/ruby
    2. 

  2. 

  3. # Find the n-th Home Prime (along with its chain).
    4. 

  4. 

  5. # Definition:
    6. 

  6. #   Home primes: for n >= 2, a(n) = the prime that is finally reached when you start with n, concatenate its prime factors (A037276) and repeat until a prime is reached.
    7. 

  7. 

  8. # See also:
    9. 

  9. #   https://oeis.org/A037274
    10. 

  10. #   https://rosettacode.org/wiki/Home_primes
    11. 

  11. 

  12. func home_prime(n) {
    13. 

  13. 

  14.     return n if (n < 2)
    15. 

  15. 

  16.     var steps = []
    17. 

  17. 

  18.     for (var f = n.factor; true; f = n.factor) {
    19. 

  19.         steps << f
    20. 

  20.         n = Num(f.join)
    21. 

  21.         break if n.is_prime
    22. 

  22.     }
    23. 

  23. 

  24.     return steps
    25. 

  25. }
    26. 

  26. 

  27. for n in (2..20, 65) {
    28. 

  28.     var steps = home_prime(n)
    29. 

  29.     say ("HP(#{n}) = ", steps.map { .join('_') }.join(' -> '))
    30. 

  30. }
    31. 

  31. 

  32. __END__
    33. 

  33. HP(2) = 2
    34. 

  34. HP(3) = 3
    35. 

  35. HP(4) = 2_2 -> 2_11
    36. 

  36. HP(5) = 5
    37. 

  37. HP(6) = 2_3
    38. 

  38. HP(7) = 7
    39. 

  39. HP(8) = 2_2_2 -> 2_3_37 -> 3_19_41 -> 3_3_3_7_13_13 -> 3_11123771 -> 7_149_317_941 -> 229_31219729 -> 11_2084656339 -> 3_347_911_118189 -> 11_613_496501723 -> 97_130517_917327 -> 53_1832651281459 -> 3_3_3_11_139_653_3863_5107
    40. 

  40. HP(9) = 3_3 -> 3_11
    41. 

  41. HP(10) = 2_5 -> 5_5 -> 5_11 -> 7_73
    42. 

  42. HP(11) = 11
    43. 

  43. HP(12) = 2_2_3
    44. 

  44. HP(13) = 13
    45. 

  45. HP(14) = 2_7 -> 3_3_3 -> 3_3_37 -> 47_71 -> 13_367
    46. 

  46. HP(15) = 3_5 -> 5_7 -> 3_19 -> 11_29
    47. 

  47. HP(16) = 2_2_2_2 -> 2_11_101 -> 3_11_6397 -> 3_163_6373
    48. 

  48. HP(17) = 17
    49. 

  49. HP(18) = 2_3_3
    50. 

  50. HP(19) = 19
    51. 

  51. HP(20) = 2_2_5 -> 3_3_5_5 -> 5_11_61 -> 11_4651 -> 3_3_12739 -> 17_194867 -> 19_41_22073 -> 709_273797 -> 3_97_137_17791 -> 11_3610337981 -> 7_3391_4786213 -> 3_3_3_3_7_23_31_1815403 -> 13_17_23_655857429041 -> 7_7_2688237874641409 -> 3_31_8308475676071413
    52. 

  52. HP(65) = 5_13 -> 3_3_3_19 -> 11_13_233 -> 11_101203 -> 3_3_23_53629 -> 3_3_1523_24247 -> 3_3_3_7_47_3732109 -> 11_18013_16843763 -> 151_740406071813 -> 3_13_13_54833_5458223 -> 3_3_97_179_373_7523_71411 -> 1571_1601_1350675311441 -> 3_3_13_33391_143947_279384649 -> 11_23_204069263_6417517893491 -> 7_11_1756639_83039633268945697 -> 29_29_5165653_13503983_12122544283 -> 228345060379_1282934064985326977 -> 3_3_3_2979253_3030445387_9367290955541 -> 1381_3211183211_75157763339900357651
    53. 

  53.