A340959 Table read by antidiagonals of the smallest prime >= n^k, n >= 1 and k >= 0.

2, 2, 2, 2, 2, 2, 2, 3, 5, 2, 2, 5, 11, 11, 2, 2, 5, 17, 29, 17, 2, 2, 7, 29, 67, 83, 37, 2, 2, 7, 37, 127, 257, 251, 67, 2, 2, 11, 53, 223, 631, 1031, 733, 131, 2, 2, 11, 67, 347, 1297, 3137, 4099, 2203, 257, 2, 2, 11, 83, 521, 2411, 7789, 15629, 16411, 6563

Offset: 1

Author

Donald S. McDonald, Jan 31 2021

Keywords

• nonn
• tabl

Examples

			Table begins:
  2, 2,  2,   2,   2,    2, ...
  2, 2,  5,  11,  17,   37, ...
  2, 3, 11,  29,  83,  251, ...
  2, 5, 17,  67, 257, 1031, ...
  2, 5, 29, 127, 631, 3137, ...
  ...;
yielding the triangle:
  2;
  2, 2;
  2, 2,  2;
  2, 3,  5,  2;
  2, 5, 11, 11,  2;
  2, 5, 17, 29, 17, 2;
  ...
		

Crossrefs

Cf. A104080 (n=2), A104081 (n=3), A104082 (n=4), A104083 (n=5), A104084 (n=7).

Programs

Mathematica

T[n_,k_]:=NextPrime[n^k-1];Flatten[Table[T[n-k,k],{n,11},{k,0,n-1}]] (* Stefano Spezia, Feb 01 2021 *)

PARI

T(n,k) = nextprime(n^k); \\ Michel Marcus, Feb 01 2021

Formula

T(n,k) = next_prime(n^k-1).