OFFSET
1,2
COMMENTS
Every prime occurs exactly once, and every composite occurs infinitely many times.
EXAMPLE
First seven rows:
1
2
5 3
4 2 8
17 19 6 7
15 5 2 3 32
63 38 44 23 25 30
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.
MATHEMATICA
x = {1};
(* In the remarks below, U(n) = ordered union of generations g(1), g(2), ...g(n) *)
x = {1};
x = DeleteDuplicates[Join[x, Map[x[[#[[1]]]]/(1 + x[[#[[2]]]]) &, Tuples[Range[Length[x]], {2}]]]] (* U(2) *)
x = DeleteDuplicates[Join[x, Map[x[[#[[1]]]]/(1 + x[[#[[2]]]]) &, Tuples[Range[Length[x]], {2}]]]] (* U(3) *)
x = DeleteDuplicates[Join[x, Map[x[[#[[1]]]]/(1 + x[[#[[2]]]]) &, Tuples[Range[Length[x]], {2}]]]] (* U(4) *)
v = Denominator[x]
Column[Table[Flatten[Table[Position[x, j/k], {j, 1, k - 1}]], {k, 1, 7}]]
CROSSREFS
KEYWORD
nonn,tabf,frac,more
AUTHOR
Clark Kimberling, Mar 19 2024
STATUS
approved