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%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