A377367 Rectangular array by antidiagonals: R(m,n) = least k such that 2n*prime(m)^k + 1 is prime.

1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1, 6, 4, 1, 1, 1, 10, 1, 1, 3, 1, 3, 1, 1, 2, 1, 1, 14, 1, 1, 2, 2, 3, 8, 3, 2, 1, 1, 1, 2, 1, 3, 3, 1, 11, 1, 1, 1, 1, 4, 2, 1, 1, 1, 2, 2, 4, 6, 5, 4, 1, 1

Offset

1,2

Links

Table of n, a(n) for n=1..78.

Example

Corner:
   1     1    1     2     1     1    1     3    2     1     1    1    1     3     2
   1     2    1     1     2     1    1     2    3     1     4    2    1     2     1
   1     1    1     4     1     1    3     3    1     1     1    8    1     3    11
   1     1    1    10     2     8    1     2    3     2     1    1    1     1     8
   1     1    1     1     3    11    2     1    2     4     1    8    1     1     1
   6     1    1     2     1     4    1    13    2     1     1    2    3     3     1
   3    14    1     1     6     1    1     3    1     1     8    1    4     2     3
   1     1    1     5     4     7    1    14    2     1     2    1    2     1     6
   1     1    4     1     3     2    1     2    3     2     5    1    6     1     2
   4     1    1     2     2     1    3     5    1     5     1    1    1     1     4
   1     1    2     3     1     2    3     2    3     1     9    1    3     1     1
   1     3    2     2     4     1    1     7    1    11     4    1    1    10     3
   1     1    2     3     3     1    1     3    1     1     1    2    1     1     2
   2     1    2     3     1     8    1     1    1     2     3    1    1     2     1
   1    16    1     4    11     1    4     3    3     2    18    1    2     4     2

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, 2, 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 *)

Crossrefs

Cf. A000040, A377366.

Sequence in context: A329041 A238744 A030421 * A085021 A060209 A037830

Adjacent sequences: A377364 A377365 A377366 * A377377 A377379 A377380

Keyword

nonn,tabl,new

Author

Clark Kimberling, Oct 31 2024

Status

approved