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%I #4 Mar 22 2024 17:40:45
%S 1,2,5,3,4,2,8,17,10,6,7,15,5,2,3,32,63,38,44,23,25,30
%N Irregular triangular array: row n shows the positions of fractions having denominator n in the array defined in A371280.
%C Every prime occurs exactly once, and every composite occurs infinitely many times.
%e First seven rows:
%e 1
%e 2
%e 5 3
%e 4 2 8
%e 17 19 6 7
%e 15 5 2 3 32
%e 63 38 44 23 25 30
%e In the array defined in A371280, the fractions 1/6, 2/6, 3/6, 4/6, 5/6 occur in positions 15, 5, 2, 3, 32, this being row 5 of the present array.
%t x = {1};
%t (* In the remarks below, U(n) = ordered union of generations g(1), g(2), ...g(n) *)
%t x = {1};
%t x = DeleteDuplicates[Join[x, Map[x[[#[[1]]]]/(1 + x[[#[[2]]]]) &, Tuples[Range[Length[x]], {2}]]]] (* U(2) *)
%t x = DeleteDuplicates[Join[x, Map[x[[#[[1]]]]/(1 + x[[#[[2]]]]) &, Tuples[Range[Length[x]], {2}]]]] (* U(3) *)
%t x = DeleteDuplicates[Join[x, Map[x[[#[[1]]]]/(1 + x[[#[[2]]]]) &, Tuples[Range[Length[x]], {2}]]]] (* U(4) *)
%t v = Denominator[x]
%t Column[Table[Flatten[Table[Position[x, j/k], {j, 1, k - 1}]], {k, 1, 7}]]
%Y Cf. 371280.
%K nonn,tabf,frac,more
%O 1,2
%A _Clark Kimberling_, Mar 19 2024
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