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Primes of the form x^2 + 2y^2 where y<=x. Terms are listed in increasing order of x; for fixed x they're in increasing order of y.
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%I #10 Jun 24 2014 01:08:33

%S 3,11,17,43,67,83,89,113,131,179,139,193,283,241,331,457,227,233,257,

%T 353,467,563,617,307,577,739,379,433,523,811,1009,443,449,491,569,641,

%U 683,953,1019,1163,547,601,691,643,787,1777,761,827,857,929,971,1307

%N Primes of the form x^2 + 2y^2 where y<=x. Terms are listed in increasing order of x; for fixed x they're in increasing order of y.

%C Every prime of the form 8n+1 or 8n+3 has a unique representation of the form x^2 + 2y^2 with positive integers x and y. This sequence has the primes for which y<=x.

%D Morris Kline, Mathematical Thought From Ancient to Modern Times, Oxford University Press 1972, p. 276 (Fermat prime number theorems).

%H Vincenzo Librandi, <a href="/A078116/b078116.txt">Table of n, a(n) for n = 1..5000</a>

%t Select[Flatten[Table[x^2+2y^2, {x, 0, 30}, {y, 0, x}]], PrimeQ]

%o (PARI) sqplus2sq(n,m) = ct=0; for(x=1,n, for(y=1,x, s = x^2+m*y^2; if(isprime(s),ct+=1; print1(s" "); ); ); ); \\ Lists primes of the form x^2+m*y^2 with 1<=y<=x<=n.

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Dec 05 2002

%E Edited by _Dean Hickerson_, Dec 12 2002