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Ilya Gutkovskiy
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Smallest n-gonal pyramidal number which can be represented as the sum of n distinct nonzero n-gonal pyramidal numbers in exactly n ways, or -1 if none exists
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prog.sf

prog.sf 2.4 KB
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  1. #!/usr/bin/ruby
    2. 

  2. 

  3. # a(n) is the smallest n-gonal pyramidal number which can be represented as the sum of n distinct nonzero n-gonal pyramidal numbers in exactly n ways, or -1 if none exists.
    4. 

  4. # https://oeis.org/A359321
    5. 

  5. 

  6. # For n = 3: 2300 = 1 + 969 + 1330 = 56 + 220 + 2024 = 165 + 364 + 1771.
    7. 

  7. # For n = 4: 6201 = 1 + 91 + 1785 + 4324 = 1 + 285 + 1015 + 4900 = 30 + 140 + 506 + 5525 = 91 + 819 + 1496 + 3795.
    8. 

  8. 

  9. # Known terms:
    10. 

  10. #   2300, 6201, 8125, 6391
    11. 

  11. 

  12. # Conjecture:
    13. 

  13. #   a(7)-a(11) are all -1.
    14. 

  14. 

  15. func isok(index, k) {
    16. 

  16. 

  17.     var n = index.pyramidal(k)
    18. 

  18.     var arr = (1..^index -> map{|j| pyramidal(j, k) })
    19. 

  19.     var s = Set(arr...)
    20. 

  20. 

  21.     var sol = []
    22. 

  22. 

  23.     arr.combinations(k-1, {|*a|
    24. 

  24.         with (n - a.sum) {|d|
    25. 

  25.             if (s.has(d) && !a.has(d)) {
    26. 

  26.                 sol << a
    27. 

  27.             }
    28. 

  28.         }
    29. 

  29.     })
    30. 

  30. 

  31.     sol.map {|a| [a..., n - a.sum].sort }.uniq
    32. 

  32. }
    33. 

  33. 

  34. func a(n) {
    35. 

  35.     for k in (1..Inf) {
    36. 

  36.         var sol = isok(k, n)
    37. 

  37.         if (sol.len == n) {
    38. 

  38.             return [n, k, k.pyramidal(n)]
    39. 

  39.         }
    40. 

  40.         elsif (sol.len > n) {
    41. 

  41.             say "[#{n}] Found #{sol.len} solutions for k = #{k}..."
    42. 

  42.         }
    43. 

  43.     }
    44. 

  44. }
    45. 

  45. 

  46. for k in (3..6) {
    47. 

  47.     say a(k)
    48. 

  48. }
    49. 

  49. 

  50. #~ say a(12)
    51. 

  51. 

  52. __END__
    53. 

  53. [7] Found 8 solutions for k = 22...
    54. 

  54. [7] Found 15 solutions for k = 26...
    55. 

  55. [7] Found 9 solutions for k = 27...
    56. 

  56. [7] Found 18 solutions for k = 28...
    57. 

  57. [7] Found 12 solutions for k = 29...
    58. 

  58. [7] Found 20 solutions for k = 30...
    59. 

  59. [7] Found 27 solutions for k = 31...
    60. 

  60. [7] Found 44 solutions for k = 32...
    61. 

  61. [7] Found 42 solutions for k = 33...
    62. 

  62. [7] Found 46 solutions for k = 34...
    63. 

  63. [7] Found 46 solutions for k = 35...
    64. 

  64. [7] Found 70 solutions for k = 36...
    65. 

  65. [7] Found 85 solutions for k = 37...
    66. 

  66. [7] Found 81 solutions for k = 38...
    67. 

  67. [7] Found 88 solutions for k = 39...
    68. 

  68. 

  69. [8] Found 10 solutions for k = 23...
    70. 

  70. [8] Found 18 solutions for k = 24...
    71. 

  71. [8] Found 14 solutions for k = 25...
    72. 

  72. [8] Found 24 solutions for k = 26...
    73. 

  73. [8] Found 17 solutions for k = 27...
    74. 

  74. [8] Found 28 solutions for k = 28...
    75. 

  75. [8] Found 53 solutions for k = 29...
    76. 

  76. 

  77. [9] Found 14 solutions for k = 26...
    78. 

  78. [9] Found 23 solutions for k = 27...
    79. 

  79. [9] Found 22 solutions for k = 28...
    80. 

  80. [9] Found 36 solutions for k = 29...
    81. 

  81. 

  82. [10] Found 11 solutions for k = 26...
    83. 

  83. [10] Found 17 solutions for k = 27...
    84. 

  84. [10] Found 11 solutions for k = 28...
    85. 

  85. [10] Found 34 solutions for k = 29...
    86. 

  86. 

  87. [11] Found 12 solutions for k = 27...
    88. 

  88. [11] Found 15 solutions for k = 29...
    89. 

  89. [11] Found 32 solutions for k = 30...
    90. 

  90. 

  91. [12] Found 33 solutions for k = 31...
    92. 

  92.