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A238048
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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.
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3
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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
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OFFSET
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1,1
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COMMENTS
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Prime 2 is not contained in this array.
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LINKS
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EXAMPLE
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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, ...
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MAPLE
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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);
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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