OFFSET

1,1

COMMENTS

Prime 2 is not contained in this array.

LINKS

Alois P. Heinz, Antidiagonals n = 1..150, flattened

EXAMPLE

Column k=3 contains prime 47 because (47+3)^2+3 = 2503 is prime.

Square array A(n,k) begins:

3, 7, 5, 3, 7, 5, 3, 7, ...

5, 13, 7, 11, 31, 13, 5, 13, ...

13, 19, 11, 13, 43, 19, 11, 43, ...

19, 31, 19, 23, 67, 29, 19, 73, ...

23, 37, 47, 29, 73, 59, 23, 79, ...

53, 43, 59, 31, 109, 73, 29, 103, ...

73, 79, 61, 41, 157, 83, 31, 109, ...

83, 97, 67, 43, 163, 103, 41, 127, ...

MAPLE

A:= proc(n, k) option remember; local p;

p:= `if`(n=1, 1, A(n-1, k));

do p:= nextprime(p);

if isprime((p+k)^2+k) then return p fi

od

end:

seq(seq(A(n, 1+d-n), n=1..d), d=1..11);

MATHEMATICA

A[n_, k_] := A[n, k] = Module[{p}, For[p = If[n == 1, 1, A[n-1, k]] // NextPrime, True, p = NextPrime[p], If[PrimeQ[(p+k)^2+k], Return[p]]]]; Table[Table[A[n, 1+d-n], {n, 1, d}], {d, 1, 11}] // Flatten (* Jean-François Alcover, Jan 19 2015, after Alois P. Heinz *)

CROSSREFS

AUTHOR

Alois P. Heinz, Feb 17 2014

STATUS

approved