A307693 -id:A307693 - cp's OEIS frontend

A327314 Rectangular array read by descending antidiagonals: the distinct rows of the quotient array, A307693, of A003188.

1, 3, 1, 2, 2, 1, 6, 4, 3, 1, 7, 5, 2, 2, 1, 5, 3, 5, 4, 2, 1, 4, 8, 6, 3, 5, 2, 1, 12, 9, 4, 7, 4, 4, 3, 1, 13, 10, 10, 9, 3, 3, 2, 3, 1, 15, 7, 11, 8, 9, 8, 6, 2, 2, 1, 14, 6, 12, 6, 10, 9, 7, 6, 5, 2, 1, 10, 16, 8, 5, 11, 7, 5, 5, 4, 4, 2, 1, 11, 17, 9

Offset: 1

Clark Kimberling, Nov 01 2019

Each row of the quotient array, A307693, occurs infinitely many times. Specifically, if p is a prime (A000040), then for every multiple m*p of p, the rows numbered m*p are identical. In the present array only the first occurrence of each row of A307693 is retained; these are the prime-numbered rows of A307693. Every row is a permutation of the positive integers, so that every positive integer occurs infinitely many times.

			Northwest corner:
  1   3   2   6   7   5   4   12  13  15
  1   2   4   5   3   8   9   10   7   6
  1   3   2   5   6   4  10   11  12   8
  1   2   4   3   7   9   8    6   5  14
  1   2   5   4   3   9  10   11   8   7
  1   2   4   3   8   9   7    6   5  15

Cf. A000040, A003188, A307693.

s = Table[BitXor[n, Floor[n/2]], {n, 2000}]; (* A003188 *)
g[n_] := Flatten[Position[Mod[s, n], 0]];
u[n_] := s[[g[Prime[n]]]]/Prime[n];
Column[Table[Take[u[n], 20], {n, 1, 20}]]  (* A326925 array *)
v[n_, k_] := u[n][[k]];
Table[v[n - k + 1, k], {n, 14}, {k, n, 1, -1}] // Flatten  (* A326925 sequence *)

cp's OEIS Frontend

A327314 Rectangular array read by descending antidiagonals: the distinct rows of the quotient array, A307693, of A003188.

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