A238048 - OEIS

%I #25 Dec 15 2015 00:56:05

%S 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,

%T 43,73,7,5,19,67,29,59,79,83,11,13,11,29,73,31,61,97,89,3,23,43,19,59,

%U 109,41,67,103,109,13,17,29,73,23,73,157,43,71,109,149

%N 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.

%C Prime 2 is not contained in this array.

%H Alois P. Heinz, <a href="/A238048/b238048.txt">Antidiagonals n = 1..150, flattened</a>

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

%e Square array A(n,k) begins:

%e    3,  7,  5,  3,   7,   5,  3,   7, ...

%e    5, 13,  7, 11,  31,  13,  5,  13, ...

%e   13, 19, 11, 13,  43,  19, 11,  43, ...

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

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

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

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

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

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

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

%p       do p:= nextprime(p);

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

%p       od

%p     end:

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

%t 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_ *)

%Y Column k=1 gives A157468.

%Y Cf. A238086.

%K nonn,tabl,look

%O 1,1

%A _Alois P. Heinz_, Feb 17 2014