A377366 Rectangular array by antidiagonals: R(m,n) = least k such that 2n*prime(m)^k - 1 is prime.

1, 1, 1, 1, 1, 4, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 2, 4, 2, 3, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 6, 2, 1, 1, 1, 2, 1, 2, 1, 5, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 2, 2, 1, 4, 10, 4, 6, 2, 1, 2, 1

Offset: 1

Author

Clark Kimberling, Oct 31 2024

Keywords

• nonn
• tabl

Examples

			Corner:
   1    1    1     2    1    1     4    1    2    2     1    1     2    3    1    2
   1    1    1     1    1    2     1    1    1    1     2    1     2    1    1    3
   4    1    1     2    3    1     2    1    1    2     1    2     4    1    1    8
   1    1    4     1    1    2     1    1    1    3     1    1     2    1    1    2
   2    1    2     1    1    2     1    4    1    1     1    3    18    1    2    1
   2    2    1     2    1    1    10    1    1    1     2    1     2    6    1    2
   2    1    1     2    2    4     1    4    2    1     3    7     1    4    1    8
   1    1    1     1    6    6     1    2    3    1     1    1    11    1    6    1
   6    5    1     2    1    1     2    4    7    1     2    1     2    1    3    4
   1    3    1    10    1    1     2    1    2    6     2    1     2    5    8    2
   1    2    1     1    1    1     1    1    9    1     2    1     1    2    3    2
   1    3    4     1    3    14    1    1    2    1     8    7     2    1    1    3
   2    1    1     1    4    2     3    1    1    2    14    7     1    6    2    1
   2    1    1     1    1    1     1    1    2    7     3    1     4    3    1    3
   4    1    1     1    2    2     1    3    1    2     1    7     8    1    1    1
   1    1    8    15    1    2     4    1    9    4     1    1     2    1    1    2
		

Crossrefs

Cf. A000040, A377367.

Programs

Mathematica

f[m_, n_, k_] := 2 n*Prime[m]^k - 1;
s[m_, n_] := Select[Range[20], PrimeQ[f[m, n, #]] &, 1]
u[m_] := Flatten[Table[s[m, n], {n, 1, 60}]]
Column[Table[Take[u[m], 16], {m, 1, 16}]]
r[m_] := Take[u[m], 12]; w[m_, n_] := r[m][[n]];
Table[w[m, n], {m, 1, 16}, {n, 1, 12}] (* array *)
Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten  (* sequence *)