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%I #23 Feb 12 2023 20:22:22
%S 5,17,37,101,197,257,401,577,677,1297,1601,2917,3137,4357,5477,7057,
%T 8101,8837,12101,13457,14401,15377,15877,16901,17957,21317,22501,
%U 24337,25601,28901,30977,32401,33857,41617,42437,44101,50177,52901,55697
%N Primes of the form 4*k^2 + 1.
%C Except for the initial 2 in A002496 this sequence is the same as A002496.
%C The prime factors of numbers of the form 4k^2 + 1 (a sum of two squares) are of the form 4m + 1.
%H Vincenzo Librandi, <a href="/A121326/b121326.txt">Table of n, a(n) for n = 1..10000</a>
%e For k=4, 4k^2 + 1 = 17, a prime.
%t Select[Table[4n^2+1,{n,0,800}],PrimeQ] (* _Vincenzo Librandi_, Dec 02 2011 *)
%o (PARI) for(x=1,200,y=4*x^2+1;if(isprime(y),print1(y",")))
%o (Magma) [a: n in [0..400] | IsPrime(a) where a is 4*n^2+1]; // _Vincenzo Librandi_, Dec 02 2011
%Y Cf. A002496.
%K nonn,easy
%O 1,1
%A _Cino Hilliard_, Aug 26 2006
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