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
Examples
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, ...
Links
- Alois P. Heinz, Antidiagonals n = 1..150, flattened
Programs
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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 *)
Comments