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A264790 Numbers k such that k^2 + 17 is prime.

%I A264790 #27 Feb 16 2025 08:33:27
%S A264790 0,6,24,60,66,78,90,108,144,162,174,186,234,252,294,300,318,330,336,
%T A264790 342,372,396,420,438,456,462,468,498,528,594,636,648,654,672,720,750,
%U A264790 798,804,834,858,888,924,930,966,984,990,1014,1026,1032,1086,1158,1194,1200
%N A264790 Numbers k such that k^2 + 17 is prime.
%C A264790 Primes of the form k^2 + 17 have a representation as a sum of 2 squares because they belong to A002144.
%C A264790 All terms are multiple of 6.
%H A264790 Daniel Starodubtsev, <a href="/A264790/b264790.txt">Table of n, a(n) for n = 1..5000</a>
%H A264790 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Near-SquarePrime.html">Near-Square Prime</a>
%F A264790 A000005(A241847(a(n))) = 2.
%F A264790 A241847(a(n)) = A228244(n).
%e A264790 a(3) = 24 because 24^2 + 17 = 593, which is prime.
%t A264790 Select[Range[0, 1200], PrimeQ[#^2 + 17] &] (* _Michael De Vlieger_, Nov 25 2015 *)
%o A264790 (PARI) for(n=0, 1e3, if(isprime(n^2+17), print1(n, ", "))) \\ _Altug Alkan_, Nov 25 2015
%o A264790 (Magma) [n: n in [0..1200 ] | IsPrime(n^2+17)]; // _Vincenzo Librandi_, Nov 25 2015
%Y A264790 Cf. A228244 (associated primes).
%Y A264790 Other sequences of the type "Numbers n such that n^2 + k is prime": A005574 (k=1), A067201 (k=2), A049422 (k=3), A007591 (k=4), A078402 (k=5), A114269 (k=6), A114270 (k=7), A114271 (k=8), A114272 (k=9), A114273 (k=10), A114274 (k=11), A114275 (k=12), A113536 (k=13), A121250 (k=14), A121982 (k=15), A122062 (k=16).
%K A264790 nonn
%O A264790 1,2
%A A264790 _Ilya Gutkovskiy_, Nov 25 2015
%E A264790 Edited by _Bruno Berselli_, Nov 26 2015