A238048 Square array A(n,k), n>=1, k>=1, read by antidiagonals, where column k is the increasing list of all primes p such that (p+k)^2+k is also prime.

3, 7, 5, 5, 13, 13, 3, 7, 19, 19, 7, 11, 11, 31, 23, 5, 31, 13, 19, 37, 53, 3, 13, 43, 23, 47, 43, 73, 7, 5, 19, 67, 29, 59, 79, 83, 11, 13, 11, 29, 73, 31, 61, 97, 89, 3, 23, 43, 19, 59, 109, 41, 67, 103, 109, 13, 17, 29, 73, 23, 73, 157, 43, 71, 109, 149

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

Column k=1 gives A157468.

Cf. A238086.

Sequence in context: A084726 A107738 A341628 * A010624 A019638 A116535

Adjacent sequences: A238045 A238046 A238047 * A238049 A238050 A238051

Keyword

nonn,tabl,look

Author

Alois P. Heinz, Feb 17 2014

Status

approved