A121326 Primes of the form 4*k^2 + 1.

5, 17, 37, 101, 197, 257, 401, 577, 677, 1297, 1601, 2917, 3137, 4357, 5477, 7057, 8101, 8837, 12101, 13457, 14401, 15377, 15877, 16901, 17957, 21317, 22501, 24337, 25601, 28901, 30977, 32401, 33857, 41617, 42437, 44101, 50177, 52901, 55697

Offset: 1

Author

Cino Hilliard, Aug 26 2006

Keywords

• nonn
• easy

Comments

Except for the initial 2 in A002496 this sequence is the same as A002496.

The prime factors of numbers of the form 4k^2 + 1 (a sum of two squares) are of the form 4m + 1.

Examples

			For k=4, 4k^2 + 1 = 17, a prime.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002496.

Programs

Magma

[a: n in [0..400] | IsPrime(a) where a is 4*n^2+1]; // Vincenzo Librandi, Dec 02 2011

Mathematica

Select[Table[4n^2+1,{n,0,800}],PrimeQ] (* Vincenzo Librandi, Dec 02 2011 *)

PARI

for(x=1,200,y=4*x^2+1;if(isprime(y),print1(y",")))