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%I #24 Nov 04 2015 11:18:07
%S 83,179,227,347,419,467,491,563,587,659,827,971,1019,1091,1259,1427,
%T 1499,1667,1811,1907,1979,2027,2243,2267,2339,2531,2579,2699,2819,
%U 2843,2939,3347,3539,3659,3779,3851,4019,4091,4259,4451,4523,4547,4691,4787,5099
%N Primes of the form p^2 + q^2 + r^2, where p,q,r are distinct primes.
%C All terms are congruent to 5 modulo 6. Smallest of primes p, q, r is always 3. - _Zak Seidov_, Jun 03 2014
%C The number of such representations of a prime of that form is A263723. - _Jonathan Sondow_ and _Robert G. Wilson v_, Nov 02 2015
%H Charles R Greathouse IV, <a href="/A182479/b182479.txt">Table of n, a(n) for n = 1..10000</a>
%e 5099 = 3^2 + 7^2 + 71^2.
%t mx = 20; ps = Prime[Range[2, mx + 1]]; t = Table[ps[[i]]^2 + ps[[j]]^2 + ps[[k]]^2, {i, mx}, {j, i + 1, mx}, {k, j + 1, mx}]; Select[Union[Flatten[t]], # <= 34 + ps[[-1]]^2 && PrimeQ[#] &] (* _T. D. Noe_, May 01 2012 *)
%o (PARI) list(lim)=my(v=List(),t);lim\=1;forprime(p=7,sqrt(lim), forprime(q=5,min(sqrtint(lim-p^2-9),p-1), t=p^2+q^2;forprime(r=3,min(sqrtint(lim-t),q-1), if(isprime(t+r^2), listput(v,t+r^2))))); vecsort(Vec(v),,8)
%o \\ _Charles R Greathouse IV_, May 01 2012
%Y Cf. A123592, A123597, A137365, A263723.
%Y Cf. A137364 (the same with repetitions). - _Zak Seidov_, Jun 03 2014
%K nonn
%O 1,1
%A _Alex Ratushnyak_, May 01 2012
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