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

1,1

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

Links

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A142332 A111078 A106962 * A182479 A106094 A142443

Adjacent sequences: A137361 A137362 A137363 * A137365 A137366 A137367

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Apr 09 2008

Extensions

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

Status

approved