A360206 Triangular array T(m,n) read by antidiagonals: T(m,n) = prime(m+n) - prime(m) - prime(n).

-1, 0, 1, 0, 3, 3, 2, 3, 5, 5, 0, 3, 3, 5, 7, 2, 3, 5, 9, 7, 11, 0, 3, 7, 7, 9, 11, 9, 2, 7, 7, 11, 11, 11, 11, 15, 4, 5, 9, 11, 9, 11, 13, 17, 15, 0, 5, 7, 7, 7, 11, 13, 13, 15, 13, 4, 7, 7, 9, 11, 15, 13, 17, 17, 13, 17, 2, 3, 5, 9, 11, 11, 13, 15, 13, 13

Offset: 1

Author

Clark Kimberling, Jan 30 2023

Keywords

• tabl
• sign

Examples

			First seven rows:
  -1
   0    1
   0    3   3
   2    3   5   5
   0    3   3   3   7
   2    3   5   9   7   11
   0    3   7   7   9   11   9
T(4,3) = prime(7) - prime(4) - prime(3) = 17 - 7 - 5 = 5.
		

Crossrefs

Cf. A000040, A066066 (right diagonal).

Programs

Mathematica

p[n_] := Prime[n];
t = Table[p[m + n] - p[m] - p[n], {m, 1, 15}, {n, 1, m}]
Flatten[t]    (* A360206 sequence *)
TableForm[t]  (* A360206 array *)

Formula

T(m,n) = prime(m+n) - prime(m) - prime(n).