A370094 Rectangular array read by antidiagonals: A(n,k) = prime(A114537(n,k)).

2, 3, 7, 5, 17, 13, 11, 59, 41, 19, 31, 277, 179, 67, 23, 127, 1787, 1063, 331, 83, 29, 709, 15299, 8527, 2221, 431, 109, 37, 5381, 167449, 87803, 19577, 3001, 599, 157, 43, 52711, 2269733, 1128889, 219613, 27457, 4397, 919, 191, 47, 648391, 37139213

Offset: 1

Author

Clark Kimberling, Feb 09 2024

Keywords

• nonn
• tabl

Comments

The rows and columns are all increasing, and every prime occurs exactly once.

Examples

			Corner:
   2    3      5     11      31      127       709
   7    17    59    277    1787    15299    167449
  13    41   179   1063    8527    87803   1128889
  19    67   331   2221   19577   219613   3042161
  23    83   431   3001   27457   318211   4535189
  29   109   599   4397   42043   506683   7474967
		

Crossrefs

Cf. A000040, A007821, A114537.

Programs

Mathematica

NonPrime[n_] := FixedPoint[n + PrimePi@# + 1 &, n];
t[n_, k_] := Nest[Prime, NonPrime[n], k];
Table[Prime[t[n - k, k]], {n, 0, 9}, {k, n, 0, -1}] // Flatten
Table[Prime[t[n, k]], {n, 0, 6}, {k, 0, 10}] // TableForm
(* after Robert G. Wilson v in A114537 *)

Formula

Let f(n) = A007821(n) and p(n) = prime(n). Row n of the array begins with f(n), followed by p(f(n)), p(p(f(n))), p(p(p(f(n)))), ...

Also, removing column 1 of array A114537 leaves the present array.