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 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.
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
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Nov 01 2019
STATUS
approved