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A087877 Primes of the form (4n+1)^2 + (4m)^2, m,n = 0,1,2.. 0

%I #4 Oct 01 2013 17:57:44

%S 17,41,89,97,233,257,281,313,337,353,401,433,457,569,577,601,641,769,

%T 809,857,881,953,1049,1097,1153,1193,1201,1297,1321,1409,1433,1489,

%U 1601,1697,1873,1889,2017,2081,2089,2113,2137,2153,2281,2377,2393,2417,2441

%N Primes of the form (4n+1)^2 + (4m)^2, m,n = 0,1,2..

%C If an odd number is of the form a^2 + b^2, then a and b must be one of the following forms.

%C a=4n+1, b=4m so that a^2+b^2 = 16(m^2+n^2) + 8n + 1 of form 4k1+1

%C a=4n+3, b=4m a^2+b^2 = 16(m^2+n^2) + 24n + 1 of form 4k2+1

%C a=4n+1, b=4m+2 a^2+b^2 = 16(m^2+n^2) + 8(n+2m ) + 5 of form 4k3+1

%C a=4n+3, b=4m+2 a^2+b^2 = 16(m^2+n^2) + 8(3n+2m) + 13 of form 4k4+1

%C The sequences built using these 4 forms produce all prime numbers of the form 4k+1.This particular sequence is a=4n+1, b=4m.

%K nonn

%O 1,1

%A _Cino Hilliard_, Oct 11 2003

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