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

1,2

Comments

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 A037693 is retained; these are the prime-numbered rows of A037693. Every row is a permutation of the positive integers, so that every positive integer occurs infinitely many times.

Links

Table of n, a(n) for n=1..81.

Example

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

Mathematica

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 *)

Crossrefs

Cf. A000040, A003188, A307693.

Sequence in context: A115110 A066635 A016568 * A021888 A115310 A236172

Adjacent sequences: A327311 A327312 A327313 * A327315 A327316 A327317

Keyword

nonn,tabl

Author

Clark Kimberling, Nov 01 2019

Status

approved