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
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
Programs
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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
Comments