A182479 Primes of the form p^2 + q^2 + r^2, where p,q,r are distinct primes.
83, 179, 227, 347, 419, 467, 491, 563, 587, 659, 827, 971, 1019, 1091, 1259, 1427, 1499, 1667, 1811, 1907, 1979, 2027, 2243, 2267, 2339, 2531, 2579, 2699, 2819, 2843, 2939, 3347, 3539, 3659, 3779, 3851, 4019, 4091, 4259, 4451, 4523, 4547, 4691, 4787, 5099
Offset: 1
Keywords
Examples
5099 = 3^2 + 7^2 + 71^2.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Mathematica
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 *) -
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) \\ Charles R Greathouse IV, May 01 2012
Comments