A371353 Irregular triangular array: row n shows the positions of fractions having denominator n in the array defined in A371280.

1, 2, 5, 3, 4, 2, 8, 17, 10, 6, 7, 15, 5, 2, 3, 32, 63, 38, 44, 23, 25, 30

Offset

1,2

Comments

Every prime occurs exactly once, and every composite occurs infinitely many times.

Links

Table of n, a(n) for n=1..22.

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

Cf. 371280.

Sequence in context: A359684 A030660 A253720 * A372388 A309735 A275726

Adjacent sequences: A371350 A371351 A371352 * A371354 A371355 A371356

Keyword

nonn,tabf,frac,more

Author

Clark Kimberling, Mar 19 2024

Status

approved