A137364 Prime numbers n such that n = p1^2 + p2^2 + p3^2, a sum of squares of 3 distinct prime numbers.

83, 179, 227, 347, 419, 419, 467, 491, 563, 587, 659, 659, 827, 971, 1019, 1019, 1091, 1259, 1427, 1499, 1499, 1667, 1811, 1811, 1907, 1907, 1979, 1979, 2027, 2243, 2267, 2339, 2339, 2531, 2579, 2699, 2819, 2843, 2939, 3347, 3539, 3539, 3659, 3659, 3779

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Apr 09 2008

Keywords

• nonn
• easy

Comments

Multiple solutions with different sets {p1,p2,p3} are indicated by repeating the entry for each solution. - R. J. Mathar, Apr 12 2008

All terms are congruent to 5 modulo 6. The smallest of the primes {p1,p2,p3} is always 3. - Zak Seidov, Jun 03 2014

Examples

			83 = 3^2 + 5^2 + 7^2;
179 = 3^2 + 7^2 + 11^2;
227 = 3^2 + 7^2 + 13^2.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A182479, A243342. - Zak Seidov, Jun 03 2014

Programs

Mathematica

Array[r, 99]; Array[y, 99]; For[i = 0, i < 10^2, r[i] = y[i] = 0; i++ ]; z = 4^2; n = 0; For[i1 = 1, i1 < z, a = Prime[i1]; a2 = a^2; For[i2 = i1 + 1, i2 < z, b = Prime[i2]; b2 = b^2; For[i3 = i2 + 1, i3 < z, c = Prime[i3]; c2 = c^2; p = a2 + b2 + c2; If[PrimeQ[p], Print[a2, " + ", b2, " + ", c2, " = ", p]; n++; r[n] = p]; i3++ ]; i2++ ]; i1++ ]; Sort[Array[r, 39]]
lst= {}; Do[p = Prime[q]^2 + Prime[r]^2 + Prime[s]^2; If[PrimeQ@p, AppendTo[lst, p]], {q, 26}, {r, q-1}, {s, r-1}]; Take[Sort@lst,72] (* Vincenzo Librandi, Jun 15 2013 *)

Extensions

More terms from R. J. Mathar, Apr 12 2008